Science Chapter 3 - Gravitation

Answer:

i. Value of gravitational constant on the earth is 6.67×10⁻¹¹ m³ kg⁻¹ s⁻²
ii. Value of gravitational constant on the Moon is 6.67×10⁻¹¹ m³ kg⁻¹ s⁻²

Answer:

Gravitational force is responsible for the moon to revolve around the earth.

Answer:

No, acceleration produced in a freely falling body does not depend on the mass of the body.

Answer:

Johannes Kepler gave the three laws of planetary motion.

Answer:

Sir Isaac Newton explained the motion of planets on the basis of gravitational force between the sun and the planets.

Answer:

Kepler’s second law is represented by the given relation, which states that “each planet revolves around the sun in such a way that the line joining the planet to the sun sweeps over equal areas in equal intervals of time.

Answer:

The third law of Kepler’s planetary motion (i.e. The law of harmonies) led Newton to establish the inverse – square rule for gravitational force between two bodies.

Answer:

The earth’s large mass is responsible for the extremely small acceleration produced in it as a result of attraction by other small objects.

Answer:

The acceleration produced in a freely falling body of mass 10 kg would be 9.8m/s².

Answer:

Gravitational force of the earth accelerates an object when it is dropped from a height.

Answer:

$\mathrm{F}=\frac{\mathrm{GMm}}{{\mathrm{d}}^2}$
where,
F − gravitational force
G − gravitational constant
M − mass of the earth
m − mass of object
d − distance

Answer:

Gravitational force is responsible for the earth’s revolution around the sun.

Answer:

Gravitational force is responsible for the attraction between two objects lying apart from each other.

Answer:

Gravitational force exerted by the moon is responsible for the formation of tides in the sea.

Answer:

Gravitational force of the sun is responsible for holding the solar system together.

Answer:

W (weight of the body) =?
m (mass of the body) = 1 kg
g (acceleration due to gravity) = 9.8 m/s²
W= mg
   = 1 × 9.8
   = 9.8 N
Answer: Weight = 9.8 N

Answer:

Since, weight, W= mg. so weight of a body depends on:
• Mass of a body.
• Acceleration due to gravity (g) at a given place.

Answer:

As the altitude increases, the mass (m) of the body remains constant but the weight (W = mg) of the body, because of decreasing acceleration due to gravity (g), decreases with an increase in altitude.

Answer:

Only weight will vary because acceleration due to gravity (g) varies from place to place and mass remains constant.

Answer:

W (weight of the body) =?
m (mass of the body) = 10 kg
g (acceleration due to gravity) = 9.8 m/s²
W= mg
   = 10 × 9.8
   = 98 N
Answer : Weight = 98N

Answer:

W (weight of the body) = 50N
m (mass of the body) = ?
g (acceleration due to gravity) = 9.8 m/s²
W= mg
50 = m × 9.8
50 × 9.8 = m
m = 5.102kg
Answer: Mass = 5.102kg

Answer:

As we go deep into the center of the earth, the acceleration due to gravity (g) there is zero. Hence, the weight of the body will become zero.

Answer:

W (weight of the body) =?
m (mass of the body) = 50 kg
g (acceleration due to gravity) = 9.8 m/s²
W= mg
= 50 × 9.8
= 490 N
Answer: Weight = 490 N

Answer:

If the weight of a body on the earth is 6N, then its weight on the moon would be about 1N. This is  because acceleration due to gravity on the surface of the moon is 1/6^th the acceleration due to gravity on the earth’s surface.

Answer:

a) True
b) False, force of gravitation between two objects depends on their masses
c) False, the value of g on the moon is about 1/6 of its value on earth
d) False, the acceleration due to gravity acting on a freely falling body is directly proportional to the earth’s mass
e) False, the weight of an object on the moon will be 1/6 of its weight on the earth

Answer:

(a) The acceleration due to gravity on the moon is about one-sixth of that on the earth.
(b) In order to the force of gravitation between two bodies to become noticeable and cause motion, one of the bodies must have an extremely large mass.
(c) The weight of an object on earth is about six times its weight on the moon.
(d) The weight of an object on the moon is about one-sixth of its weight on the earth.
(e) The value of g on the earth is about six times of that on the moon.
(f) If the weight of a body is 6N on the moon, it will be about 36N on the earth.

Answer:

g = GM /R²     
This is an equation , which expresses acceleration due to gravity. It states that acceleration due to gravity (g) can be calculated as a product of the Gravitational Constant (G), which is 6.673 × 10⁻¹¹ Nm² kg⁻² and mass of the planet (M) i.e., 5.98 × 10²⁴ kg in case of the earth divided by square of radius of that planet (R), i.e., 6.4 ×10⁶ m for earth. This is an equation, which expresses acceleration due to gravity. By putting the respective values for earth, g can be calculated as 9.8 m/s².

Answer:

A falling body, on which only the earth’s gravity acts, is known as a freely falling body and such a fall is known as free fall.
a) No, because acceleration due to gravity (g) does not depend on the body’s mass. Thus, bodies of different mass accelerate towards the earth with same acceleration.

Answer:

Yes, according to Newton's third law of motion, “to every action, there is an equal and opposite reaction”. Now, we apply this concept to the gravitational attraction between the sun and the earth. The sun exerts a gravitational force on the earth, and thus the earth also exerts a gravitational force on the sun. Thus, they are balanced in their orbits and the earth revolves around the sun.

Answer:

The gravitational force between two cricket balls is extremely small but that between a cricket ball and the earth is large because force depends on mass of an object. Greater the mass, greater is the force of gravitation. This force of gravity is very week between the two cricket balls because of their mass, so it cannot be felt. But with the earth, it can be felt as the earth’s mass is very large.

Answer:

Gravitational force is inversely proportional to the square of the distance between the masses. More the distance, less the gravitational force; less the distance, more is the gravitational force. This is how gravitational force between two objects is dependent on the distance.

Answer:

$\mathrm{F}=\frac{\mathrm{GMm}}{{\mathrm{r}}^2}$
where,
F − gravitational force
G − gravitational constant
M − mass of the earth
m − mass of object
r − distance

(i).  r = doubled
$\mathrm{F}=\frac{\mathrm{GMm}}{{\mathrm{r}}^2}$ keeping everything constant i.e. G, M, m
$=\frac{\mathrm{GMm}}{{\left(2\mathrm{r}\right)}^2}$
$=\frac{\mathrm{GMm}}{4{\mathrm{r}}^2}$
F becomes one-fourth.
        
(ii).  r = halved

$\mathrm{F}=\frac{\mathrm{GMm}}{{\mathrm{r}}^2}$ keeping everything constant i.e. G, M, m
$=\frac{\mathrm{GMm}}{{\left(1/2\mathrm{r}\right)}^2}$
$=\frac{\mathrm{GMm}}{{\left(1/4\mathrm{r}\right)}^2}$
$=\frac{4\mathrm{GM} \mathrm{m}}{{\mathrm{r}}^2}$   
F becomes four times the original.

Answer:

Applications of universal law of gravitation,
i. Planets revolve round the sun due to gravitational force between the sun and the planets. The force required by the planets to move round in their orbit is the centripetal force, which is provided by the gravitational force of attraction between the planets and the Sun

ii. Tide is the periodic rise and fall of all ocean waters, including those of open sea, gulfs, and bays, resulting from the gravitational attraction of the Moon and the Sun upon the water and upon the Earth itself. The force that causes tides in the water of the world’s oceans and seas is mostly due to the pull of the Moon’s gravity. This pull causes the water in the oceans and seas nearest to the Moon to bulge slightly. The sea water furthest from the Moon is pulled less than elsewhere, producing another bulge here as well. There are high tides where the two bulges are, and low tides in between. As the Earth turns on its axis, places move in and out of these bulges and their sea level rises and falls.

Answer:

A stone, when released from the hand, falls towards the earth due to gravitational force. The gravitational force acts both on the stone and the earth. The stone attracts the earth with the same force by which the earth attracts the stone. Since, the stone’s mass is very small as compared to the earth’s mass, so acceleration produced in the stone is very large but that in the earth is negligible. Thus, the earth’s motion is not noticed, whereas that of the stone is.

Answer:

F (gravitational force) = ?
G (gravitational constant) = 6.7 × 10⁻¹¹ Nm² kg⁻²
M (mass of body)= 120 kg
m (mass of body) = 50 kg
d (distance from each other) = 10 m
$$\begin{gathered} \mathrm{F}=\frac{\mathrm{GMm}}{{\mathrm{d}}^2} \\ =\frac{6.7\times {10}^{-11}\times 120\times 50}{{\left(10\right)}^2} \\ =\frac{6.7\times {10}^{-11}\times 12\times 5\times \cancel{100}}{\cancel{100}} \\ =6.7\times 10 \end{gathered}$$^-11×12×5   =402×10^-11N   =4.02×10^-9N Answer: F=4.02×10^-9N

Answer:

F (gravitational force) = ?
G (gravitational constant) = 6.7 × 10⁻¹¹ Nm² kg⁻²
M (mass of earth)= 6 × 10²⁴  kg
m (mass of body) = 150 kg
r (radius of earth) = 6.4 × 10⁶ m
$\mathrm{F}=\frac{\mathrm{GMm}}{{\mathrm{r}}^2}$
$$\begin{gathered} =\frac{6.7\times {10}^{-11}\times 6\times {10}^{24}\times 150}{{\left(6.4\times {10}^6\right)}^2} \\ =\frac{6.7\times {10}^{-11}\times 6\times {10}^{24}\times 150}{6.4\times 6.4\times {10}^{12}} \left({10}^{24-11}={10}^{13}\right) \\ =\frac{6.7\times 6\times 15\times {10}^{14}}{6.4\times 6.4\times {10}^{12}} \left({10}^{14-12}={10}^2\right) \\ =14.72\times 10 \end{gathered}$$² =1472N
Answer: Force of gravity = 1,472N

Answer:

F (gravitational force) = ?
G (gravitational constant) = 6.673 × 10⁻¹¹ Nm² kg⁻²
M (mass of sun) = 2×10³⁰ kg
m (mass of earth)= 6×10²⁴  kg
d (average distance between sun and earth) = 1.5×10⁸ km = 1.5 ×10⁸ ×1000 = 1.5×10¹¹m
$\mathrm{F}=\frac{\mathrm{GMm}}{{\mathrm{d}}^2}$
$$\begin{gathered} =\frac{6.673\times {10}^{-11}\times 2\times {10}^{30}\times 6\times {10}^{24}}{{\left(1.5\times {10}^{11}\right)}^2} \\ =\frac{6.673\times {10}^{-11}\times 2\times {10}^{30}\times 6\times {10}^{24}}{1.5\times 1.5\times {10}^{22}} \left({10}^{24+30-11}={10}^{43}\right) \\ =\frac{6.673\times 2\times 6\times {10}^{43}}{1.5\times 1.5\times {10}^{22}} \left({10}^{43-22}={10}^{21}\right) \\ =\frac{6.673\times 2\times 6\times {10}^{21}}{1.5\times 1.5} \left({10}^{43-22}={10}^{21}\right) \\ =\frac{80.076\times {10}^{21}}{1.5\times 1.5} \\ =35.59\times 10 \end{gathered}$$²¹ N =3.57×10²² N
Answer: Force of gravity = 3.57×10²² N

Answer:

v (final velocity) = 0 m/s
u (initial velocity) = ?
a (acceleration due to gravity i.e.,  g) = 9.8m/s²
t (time) = 3 sec
v  = u + gt
0 = u + 9.8 × 3
0 = u + 29.4
u  = −29.4m/s   
Note - Answer is in negative i.e. −29.4m/s, as it is directed opposite to the acceleration due to gravity and we have taken the motion along acceleration due to gravity as positive.
Answer: 29.4m/s

Answer:

s (distance) = ?
u (initial velocity) = 0 m/s
a (acceleration due to gravity i.e. g) = 9.8m/s²
t (time) = 2.5 sec
S = ut +1/2 gt²
= 0 ×2.5 + ½ × 9.8× 2.5× 2.5
= ½ ×9.8 ×2.5× 2.5
= 61.25×2
= 30.625 m
Answer: 30.625 m

Answer:

(i) s (distance) = 20m
u (initial velocity) = 0 m/s
a (acceleration due to gravity i.e., g) = 10m/s²
t (time) = ?
S = ut +1/2 gt²
20 = 0×t + ½ ×10 ×t²
20 = ½ ×10×t²
20×2 = 10t²
20×2 ×10 = t²
t² = 4
t = 2
Answer: time = 2 sec

(ii). v (final velocity) = ?
u (initial velocity) = 0 m/s
a (acceleration due to gravity i.e., g) = 10m/s²
t (time) = 2 sec
v = u + gt
= 0 + 10 × 2
= 20m/s
Answer: v = 20 m/s

Answer:

s (distance) = ?
v (final velocity) = 0 m/s
u (initial velocity) = −20 m/s
a (acceleration due to gravity i.e., g) = 9.8m/s²
υ² − u² = 2as
(0)² − (−20)² = 2 × 9.8 × S
−400 × 2 × 9.8 = S
S = −20.4 m
The negative sign comes because the displacement is upward and we have considered the motion along the acceleration due to gravity (downward) as positive. Thus, the required distance is 20.4 m.
Answer: s = 20.4 m

Answer:

(a) v (final velocity) = 0 m/s
u (initial velocity) = ?
a (acceleration due to gravity i.e., g) = 10 m/s²
S (distance) = 5 m
υ² − u² = 2aS
(0)² − (u)² = 2 × 10 × 5
−(u)² = 2 × 10 × 5
−(u)² = 100
u =  −10 m/s
Answer: u =  −10 m/s
Note − The initial velocity was negative i.e. −10 m/s, as it was velocity against gravity because the ball was thrown upwards. This can be neglected.
(b) s (distance) = 5m
u (initial velocity) = 10 m/s
a (acceleration due to gravity i.e., g) = 10m/s²
t (time) = ?
S = ut +1/2 gt²
⇒ 5 = 10 × t + ½ × 10 × t²
⇒ 5 = 10t + 5t²
⇒ t² + 2t − 1 = 0
⇒ t = ($\sqrt{2}$ − 1) s or (−$\sqrt{2}$ − 1) s
Since, time cannot be negative, so, the required answer is ($\sqrt{2}$ − 1) s.

Answer:

Answer:

Yes, a body can have mass but no weight at the centre of the earth. This is because acceleration due to gravity (g) decreases as we go deep into the earth and becomes zero at the centre.

Answer:

W (weight of the body) = 9.8N
m (mass of the body) = ?
g (acceleration due to gravity) = 9.8 m/s²
W= mg
9.8 = m × 9.8
9.8 /9.8 = m
1 = m
Answer: Mass = 1kg

F (force) = 20N
M (mass of body) = 1kg
F = m × a
20 = 1 × a
20/1 = a
a = 20m/s²
Answer: Acceleration = 20m/s²

Answer:

W (Weight of the stone) = 20N
m (mass of the stone) = ?
g (acceleration due to gravity) = 9.8 m/s²
W= mg
  20 = m × 9.8
   20/9.8 = m
   2.04 = m
Answer: Mass = 2.04 kg

Answer:

(i) Mass on moon = 20 kg (mass remains constant everywhere)
(ii) W (Weight of the object on moon) = ?
m (mass of the object) = 20kg
g (acceleration due to gravity on moon)= 1.6 m/s2
W= mg
= 20×1.6
= 32 N
Answer: Weight on moon = 32N

Answer:

Mass is more fundamental because it remains constant at all places, irrespective of a change in place. But weight depends on acceleration due to gravity (g), which varies with location.

Answer:

The weight of an object on the moon is 1/6^th of that on earth because the acceleration due to gravity on the moon is 1/6^th of that on earth. Therefore, weight of an object decreases on the moon.

Answer:

a) The quantity of matter contained in a body is called its mass. The SI unit of mass is kg.
b) The force with which the earth attracts a body towards its centre is called weight. The SI unit of weight is N.
c) The relation between mass and weight of a body is given by the following equation:
W = mg
Where,
m = mass of object
g = acceleration due to gravity
W = weight of a body

Answer:

a) The force of attraction between two particles or bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Isaac Newton proposed this law, which is also known as Newton’s law of gravitation.

b) Gravitational constant is defined as the force of attraction between two bodies of unit mass separated by a unit distance. Unit of gravitational constant is Nm² kg⁻².

Answer:

Uniform acceleration produced in a free falling body due to the earth’s gravitational force is known as acceleration due to gravity on earth, and is denoted by ‘g’.
(a) The usual value of acceleration due to gravity on earth is 9.8m/s².
(b) The SI unit of acceleration due to gravity is m/s².

Answer:

No, acceleration due to gravity of the earth, ‘g’, is not constant at all places. This is because the earth is not a perfect sphere, so its radius is not same at all the places on its surface. Since the radius of the earth is minimum at the poles, the value of ‘g’ is maximum at the poles. The value of ‘g’ is minimum at the equator, as the earth’s radius is maximum.
a) g = GM /R²
g (acceleration due to gravity) = ?
G (Gravitational Constant) = 6.7 × 10⁻¹¹ Nm² kg⁻²
M (mass of satellite) = 7.4×10²² kg
R (radius of satellite) = 1.74 ×10⁶ m
g = GM /R²     
$$\begin{gathered} \mathrm{g}=\frac{6.7\times {10}^{-11}\times 7.4\times {10}^{22}}{{\left(1.74\times {10}^6\right)}^2} \\ =\frac{6.7\times {10}^{-11}\times 7.4\times {10}^{22}}{{\left(1.74\times {10}^6\right)}^2} \left({10}^{22-11}={10}^{11}\right) \\ =\frac{6.7\times 7.4\times {10}^{11}}{1.74\times 1.74\times {10}^{12}} \left({10}^{11-12}={10}^{-1}\right) \\ =16.376\times 10 \end{gathered}$$^-1   =1.6 m/s²
Answer: g = 1.6m/s²
The satellite is Moon.

Answer:

Kepler’s law of motion:
a) Law of orbits – Every planet moves around the sun in an elliptical orbit, with the sun at one of the foci of the elliptical orbit.
This law means that the orbit of a planet around the sun is an ellipse and not an exact circle. An elliptical path has two foci, and the sun is at one of the two foci of elliptical path.
b) Law of areas – The line joining the sun and every planet sweeps out equal areas in equal intervals of time.
This means that a planet moves faster when it is closer to the sun, and moves slowly when it is farther from the sun.
c) Law of periods – The cube of the mean distance of a planet from the sun is directly proportional to the square of time it takes to move around the sun.

Answer:

g = GM /R²
g (acceleration due to gravity) = ?
G (Gravitational Constant) = 6.7 × 10⁻¹¹ Nm² kg⁻²
M (mass of the planet) = 6 × 10²⁴ kg
R (radius of planet) = 6.4 ×10⁶ m    
(Diameter of the planet = 12.8 × 10³ × 2 × 1000 = 6.4 ×10⁶ m)
g = GM /R²
$\mathrm{g}=\frac{ 6.{\mathrm{7\; \times 10}}^{-11}\times {\mathrm{6\times 10}}^{24}}{{(6.4\; \times 10}^6{)}^2} =\frac{6.7\times {10}^{-11}\times 6\times {10}^{24}}{{\left(6.4\times {10}^6\right)}^2} \left({10}^{24-11}={10}^{13}\right) =\frac{6.7\times 6\times {10}^{13}}{6.4\times 6.4\times {10}^{12}} \left({10}^{13-12}=10\right) =0.981\times 10 =9.8 \mathrm{m}/\mathrm{s}$²
Answer: g = 9.8 m/s²
This planet is earth.

Answer:

(b)  u² / 2g
At the maximum height 'h', the velocity becomes zero.
Using,
v^2 = u^2 − 2gh
⇒ 0 = u^2 − 2gh
⇒ h = u^2/(2g)

Answer:

(c)  Same as that of the earth
G is universal gravitational constant. So, it remains constant everywhere.

Answer:

(b) Is less than that of the earth
The value of g on moon is 1/6 times its value on the earth.

Answer:

(d)  Gravity
Gravity of the earth holds the atmosphere consisting of a large number of gases.

Answer:

(d)  universal gravitational constant

Answer:

(a)  zero, as g = 0

Answer:

(a) have same velocity at any instance
We know,
v = u + at
⇒ v = 0 + gt
[Here, g is acc. Due to gravity on moon]
Thus, the equation of velocity for a freely falling body is independent of the mass of the body.
So, different masses that are dropped simultaneously with the same or zero initial velocity will have same velocity at any instant.

Answer:

Is the least in equator
because its value decreases on moving near the equator.

Answer:

(c)  any two bodies having the same mass.

Answer:

(d) depends neither on mass nor on the radius of earth, as it is a constant in the formula for gravitational force.

Answer:

(c)  4 times
Here, m1 and m2 are doubled and r remains constant.
F = G ×m1 × m2/r²
   = G × 2m1 × 2m2/r²
    = 4 G ×m1 ×m2/r²

Answer:

(d)  is of the same value irrespective of the place of observation
This is because G is constant in the given equation.

Answer:

(d)  4x
G = x
m₁ and m₂ are constant
Since, r is reduced to half, let, r/ = r/2
Gravitation force, F = G × m₁ × m₂/r² = x
When r is reduced to half the force becomes, F/ = G × m₁ × m₂/(r/)²
= G × m₁ × m₂ /(r/2)²
= 4x

Answer:

(d)  F₁ and F₂ are exactly equal in magnitude
According to Newton's third law of motion, if an object exerts a force on another object, then the second object exerts an equal and opposite force on the first object.

Answer:

(c) r³ ∝ T²
According to Kepler’s third law of planetary motion, the cube of mean distance of a planet from the sun is directly proportional to the square of time it takes to move around the sun.

Answer:

F (gravitational force) = ?
G (gravitational constant) = G
M (mass of sun) = M
m (mass of the earth)= m
d (average distance between sun and earth) = increased by 5 times than
Rest all variables remain constant
$$\begin{gathered} \mathbf{F}\mathbf{=}\frac{\mathbf{GM}\mathbf{ }\mathbf{m}}{{\mathbf{d}}^{\mathbf{2}}} \\ \mathrm{F}=\frac{\mathrm{GM} \mathrm{m}}{{\left(5\mathrm{d}\right)}^2} \\ \mathrm{F}=\frac{\mathrm{GM} \mathrm{m}}{25 {\mathrm{d}}^2} \end{gathered}$$
(NOTE – To maintain the same gravitational force, the mass should be increased by 25 times)
$$\begin{gathered} \mathrm{F}=\frac{\mathrm{GM} \cancel{25}\mathrm{m}}{\cancel{25}{\mathrm{d}}^2} \\ \mathrm{F}=\frac{\mathrm{GM} \mathrm{m}}{{\mathrm{d}}^2} \end{gathered}$$
There would be an increase in mass.

Answer:

In order to notice the gravitational force of attraction that act between two objects, it is necessary that one of the objects should have extremely large mass as compared to the other. But none of the object has such large mass, so we cannot notice the forces.
The two objects in a room do not move towards each other because they have small mass and so the gravitational force of attraction between them is very weak.

Answer:

Mass and radius both are half of those of the earth
g (acceleration due to gravity) = ?
G (gravitational constant) = 6.673 × 10⁻¹¹ Nm² kg⁻²
M (mass of new planet)= (5.98 × 10²⁴  kg)/2
R (radius of the earth) = (6.4 × 10⁶ m)/2
$$\begin{gathered} \mathbf{g}\mathbf{=}\frac{\mathbf{GM}}{{\mathbf{R}}^{\mathbf{2}}} \\ \mathbf{ }=\frac{6.673\times {10}^{-11}\times 5.98\times {10}^{24}\times 4}{{\left(6.4\times {10}^6\right)}^2\times 2} \\ \mathbf{ }=\frac{6.673\times {10}^{-11}\times 5.98\times {10}^{24}\times 4}{6.4\times 6.4\times {10}^{12}\times 2} \left({{10}^{24}}^{-11}={10}^{13}\right) \\ \mathbf{ }=\frac{6.673\times 5.98\times 4\times {10}^{14}}{6.4\times 6.4\times {10}^{12}\times 2} \left({{10}^{13}}^{-12}=10\right) \\ \mathbf{ }=\frac{6.673\times 5.98\times 4\times 10}{6.4\times 6.4\times 2} \\ \mathbf{ }=\frac{159.61816\times 10}{6.4\times 6.4\times 2} \\ \mathbf{ }=1.9484\times 10\mathbf{ }=19.5\mathrm{N} \end{gathered}$$

Answer:

The coin will touch the ground first, because the relative air resistance on the paper is greater than on the coin (because the coin and the paper do not have the same density, so the proportion of air resistance as compared to weight is the one relevant on paper than on coin).
In a vacuum, both the coin and the piece of paper will drop at the same rate due to the absence of air resistance (their acceleration being the same).

Answer:

We see only the stone falling towards the earth but not the earth rising towards the stone because mass of the stone is negligible as compared to the earth’s mass. Hence, acceleration in the earth is negligible as compared to acceleration in stone. So, the stone falls towards the earth, but not vice-versa.

Answer:

The shape of a planet’s orbit around the sun is elliptical.
The assumption made by Newton is that the orbit of the planet around the sun is circular.

Answer:

a) As $g\propto \frac{1}{r^2}$, hence the value of g, according to the increasing distances from the earth, are as follows:
9.23 m/s², 7.34 m/s², 3.08 m/s², 1.49 m/s², 0.57 m/s², 0.30 m/s²
b)  The place would be high up in the sky because the earth’s radius is 6,400 km which is lesser than 10000 km.

Answer:

The common unit of density is g/cm³.

Answer:

The SI unit of density of water is kg/m³.

Answer:

The value of relative density of water is 1.

Answer:

Pascal (Pa) is one of the units of pressure.

Answer:

The SI unit of pressure is N/m² or pascal.

Answer:

a) False. The buoyant force depends on the volume of object immersed in the liquid and the density of the fluid.
b) True. Archimedes' principle can be applied to any fluid (liquid and gas).

Answer:

The buoyant force on an object due to a liquid acts in upward direction (i.e., upthrust).

Answer:

Buoyant force is also known as upthrust.

Answer:

Buoyant force is the force that makes heavy objects appear light when immersed in a liquid.

Answer:

Upthrust (buoyant force) is the upward force exerted by a liquid when an object is immersed in it.

Answer:

Archimedes’ principle gives us the magnitude of buoyant force acting on an object immersed in a liquid.

Answer:

According to the given statement, mercury is 13.6 times heavier than the equal volume of water.

Answer:

The thrust per unit area is called pressure.

Answer:

Buoyant force or upthrust is the scientific term for the upward force acting on an object immersed in a liquid.

Answer:

Buoyancy is an upward force exerted by a fluid that opposes the weight of an immersed object.

Answer:

Water causes buoyant force or upthrust on a boat.

Answer:

The ice floats on the water because it is less dense than water. A substance floats if it is less dense than the liquid in which it is immersed.

Answer:

Area = 0.5 m²
Pressure = 500 Pa
Thrust = ?
$\mathrm{Pressure}=\frac{\mathrm{Thrust}}{\mathrm{Area}}$
Pressure × Area = Thrust
500 × 0.5 = Thrust
250 N = Thrust
Answer: Thrust = 250 N.

Answer:

According to Archimedes’ principle, buoyant force equals the weight of the liquid displaced by the object. Therefore, the buoyant force on the object would be 200 N.

Answer:

Archimedes gave the magnitude of buoyant force acting on a solid object immersed in a liquid.

Answer:

ρ (density) = 19 g/cm³
V (volume) = ?
m (mass) = 95 g
$$\begin{gathered} \rho =\frac{m}{V} \\ V=\frac{m}{\rho } \\ =\frac{95}{19} \end{gathered}$$

V = 5 cm³
Answer: Volume of gold = 5 cm³.

Answer:

ρ (density) = 3,000 kg/m³
V (volume) = 5 m³
m (mass) = ?
$\rho =\frac{m}{V}$
ρ×V=m
3,000 × 5 = m
15,000 = m
Answer: Mass of cement = 15,000 kg.

Answer:

ρ (density) = ?
V (volume) = 10 cm³
m (mass) = 100 g
$$\begin{gathered} \rho =\frac{m}{V} \\ =\frac{100}{10} \end{gathered}$$
ρ = 10
Answer: Density of the substance = 10g/cm³.

Answer:

A wooden block held under water floats on the surface on release because it is less dense than water. A substance floats if it is less dense than the fluid in which it is immersed after the external force is withdrawn from it.

Answer:

It will float because its density is less than that of the water in the bucket.

Answer:

(a) The amount of force acting perpendicularly per unit area is called pressure.
(b) Buoyant force makes the object appear lighter in water.
(c) A heavy ship floats on water because its average density is less than that of water.
(d) In fluids (liquids and gases), pressure acts in all directions and increases as the depth increases.
(e) In order to sink in a fluid, the density of an object must be greater than the density of the fluid.
(f) Snowshoes work by distributing the person’s weight over a much bigger area.
(g) If the area of a snowshoe is five times bigger than the area of an ordinary shoe, then the pressure exerted by it would be five times smaller.

Answer:

a)

Answer:

Thrust is the force exerted on a body perpendicular to the surface. It is the total force acting on the surface of a body.
The unit of thrust is newton (N).

Answer:

In a bucket, a mug full of water appears lighter when it is under water than when it is outside the water because water exerts an upward force on the object immersed in it. Thus, the upward force acting on an object immersed in a liquid results in an apparent loss of weight, making the object to float on its surface. This upward force is called buoyant force or upthrust.

Answer:

The buoyant force increases when there is an increase in volume of solid object immersed in a liquid. The buoyant force reaches the maximum when the object is completely immersed in a liquid.

Answer:

We feel light on our feet when standing in a swimming pool with water up to our armpits because of the buoyant force. It exerts an upward force on our body and makes us feel our apparent weight which is less than our actual weight.

Answer:

During the floods, the boulders are immersed in water. The apparent weights of the boulders are less and that helps the flowing water to push and move the boulders.

Answer:

An iron nail sinks in water because the density of iron (7,900 kg/m³) is more than the density of water (1,000 kg/m³). Whereas the density of mercury (13,600 kg/m³) is more than the density of iron, so the iron nail floats in mercury.

Answer:

A piece of glass sinks in water because the density of glass (2,500 kg/m³) is more than the density of water (1,000 kg/m³). Whereas the density of mercury (13,600 kg/m³) is more than the density of glass, so the glass piece floats in mercury.

Answer:

Steel sinks in water because the density of steel is higher than water. But when steel is converted into a steel boat, it traps a lot of air and thus the average density of the steel boat is less than water. Hence, steel boat floats on water.

Answer:

Schools bags are provided with wide straps. On carrying them on our shoulders, the area under these straps enlarges, exerting a small pressure. It is due to this small pressure we feel comfortable carrying our bags on our shoulders.

Answer:

The area under the sharp knife is less than the area under the blunt knife. Hence, the pressure exerted by the sharp knife is more than the pressure exerted by the blunt knife on an object. Therefore, when a same amount of force is applied on both the knives, the sharp knife penetrates deeper into the object than the blunt knife.

Answer:

Wooden or concrete sleepers are kept below the railway line because the weight of the train is spread over a large area of the sleepers. Therefore, the pressure acting on the ground under the sleepers is reduced. This prevents the shrinking of the ground under the weight of the train.

Answer:

An army tank is a very heavy vehicle. In order to make it travel faster over different kinds of ground surfaces, they are provided with wide steel belt. This wide steel belt spreads the weight of the tank over a larger surface area by exerting a smaller pressure on ground, as we know pressure is inversely proportional to the surface area of an object.

Answer:

The tip of a sewing needle is sharp because the area under the pointed end of the sharp needle is very small. Pressure exerted by a sharp needle is more on the cloth and can pierce easily through the cloth.

Answer:

We know surface area is inversely proportional to pressure. Therefore when we stand, our body pressure is transferred equally on both the legs. Hence, the surface area increases and the pressure decrease. But when we walk, our body pressure is transferred to single leg at a time. Hence, the surface area decreases and the pressure increase. Thus, pressure is more while we walk.

Answer:

Snowshoes do not sink in soft snow because they have wide and flat surfaces. Hence, the body weight is spread over a large surface area, thereby reducing the pressure on the shoes.

Answer:

When a person stands on a cushion, the entire weight of his body gets focused on a smaller area, thereby producing a larger pressure. But when a person lies on a cushion, the entire weight is distributed over a larger area, producing a smaller pressure. Thus, the depression in the cushion is more when a person stands than when he lies.

Answer:

It is easier to walk on a soft sand by wearing a pair of flat shoes rather than a pair of high-heeled shoes because flat shoes have a larger surface area where the body weight of the person gets uniformly distributed and puts lesser pressure on sand, whereas heels have a smaller surface area where the weight of the body is focused on a smaller area and increases the pressure.

Answer:

The tip of a nail is sharp and pointed because the area under the pointed end of the sharp nail is very small. Therefore, the pressure exerted by a sharp nail is more on the wall and it can pierce easily on the wall with less amount of work done.

Answer:

The buildings and dams have wider foundations because wider the foundation, larger the surface area and smaller the pressure on the ground and thereby preventing the buildings and dams from sinking into the ground.

Answer:

Iron and steel pieces sink in water because iron and steel have higher density than water, but iron and steel ships float in water because they trap a lot of air and thereby reduce the average density of the ships (steel and iron) than water.

Answer:

Camels have large flat feet and thus a larger surface area. Hence, the pressure exerted by the camel’s large flat feet on the surface of the sand is small and the feet do not sink in sand. Therefore, they can walk easily on sand.

Answer:

a) Buoyant force.
b) Force of friction.
c) Gravitational force.
d) Reaction force.

Answer:

Area = 3 m²
Pressure = 10 Pa
Force = ?
$\mathrm{Pressure}=\frac{\mathrm{Force}}{\mathrm{Area}}$
Pressure × Area = Force
10 × 3 = Force
30 N = Force
Answer: Force = 30 N.
If the area is made one-third, then
Area = 3 m² (1/3 of 3 m²) = 1 m²
Pressure = 10 Pa
Force = ?

$\mathrm{Pressure}=\frac{\mathrm{Force}}{\mathrm{Area}}$
Pressure × Area = Force
10 × 1 = Force
10 N = Force
Answer: Force =10 N.

Answer:

Area of one foot = 160 cm² (160/10,000 = 0.016 m²)
Area of two feet = 0.016 × 2 = 0.032m²
Pressure = ?
Weight = 550 N
$$\begin{gathered} \mathrm{Pressure}=\frac{\mathrm{Force}}{\mathrm{Area}} \\ =\frac{550}{0.032} \end{gathered}$$
Pressure = 17,187.5 Pa or N/m²
Ans: Pressure = 17,187.5 Pa or N/m².

(b)
Area = 160 cm² (160/10,000 = 0.016 cm²)
Pressure = ?
Weight = 550 N
$$\begin{gathered} \mathrm{Pressure}=\frac{\mathrm{Force}}{\mathrm{Area}} \\ =\frac{550}{0.016} \end{gathered}$$

Pressure = 34,375 Pa
Answer: Pressure = 34,375 Pa or N/m².

Answer:

ρ (density) = ?
V (volume) = 3 m³
m (mass) = 9 kg
$$\begin{gathered} \rho =\frac{m}{V} \\ =\frac{9}{3} \end{gathered}$$
ρ = 3 kg/m³
Answer: Density = 3 kg/m³.
It will float in water because the density of this object (3 kg/m³) is less than the density of water (1,000 kg/m³).

Answer:

It will weigh less in water because an upward force (buoyant force) equals the weight of water displaced by it acts on the object when immersed in water which reduces its apparent weight.

Answer:

Density is defined by the following equation:
$\rho =\frac{m}{V}$,
where ρ = density,
V = volume, and
m = mass.

(b)
ρ (density of material A) = ?
V (volume of material A) = 20 cm³
m (mass of material A) = 5 kg = 5 × 1,000 = 5,000 g
$$\begin{gathered} \rho =\frac{m}{V} \\ =\frac{5,000}{20} \end{gathered}$$

ρ = 250 g/cm³
Ans: Density of material A = 250 g/cm³.

ρ (density of material B) = ?
V (volume of material B) = 90 cm³
m (mass of material B) = 20 kg = 20 × 1,000 = 20,000 g
$$\begin{gathered} \rho =\frac{m}{V} \\ =\frac{20,000}{90} \end{gathered}$$
ρ = 222.222 g/cm³
Answer: Density of material B = 222.22 g/cm³.
A has greater density.

Answer:

(a) The upward force exerted by a liquid on a body when immersed in a liquid is known as buoyant force. The buoyant force depends on the following factors:
(i) Size or volume of the body immersed in a liquid.
(ii) The density of the liquid in which the body is immersed.
Buoyant force is exerted by the pressure difference in the surrounding medium caused by gravity.

(b) F (force) = ?
m (mass)= 600 kg
a (acceleration due to gravity) = 10 m/s²

F = m × a
   = 600 × 10
   = 6,000 N
Ans: Buoyant force acting on a boat = 6,000 N.

Answer:

(a) Principle of flotation – It is the other name of Archimedes' Principle. the upthrust or the buoyant force is equal to the weight of the liquid displaced by the body. This is known as Archimedes’ principle.
Archimedes principle states that when a body is immersed wholly or partially in a liquid, it experiences an upward buoyant force of magnitude equal to the weight of the liquid displaced by it.

Buoyant force = Weight of displaced liquid

(b) (i) Buoyant force = 6,000 N. (According to Archimedes’ principle, buoyant force is equal to the weight of the liquid displaced by the body.)
(ii) Weight of the boat = 6,000 N. (According to Archimedes’ principle, weight of the boat is equal to the amount of the water displaced by the body.)

Answer:

(a) Density is defined as the mass per unit volume of a substance. The symbol for density is ρ. Mathematically, density is defined as
$\mathrm{\rho }=\frac{m}{V}$
The SI unit of density is kg/m³.

(b) Relative density of a substance is the ratio of density of the substance to the density of water. Relative density has no unit.

(c)
$$\begin{gathered} \mathrm{Relative} \mathrm{density}=\frac{\mathrm{Density} \mathrm{of} \mathrm{turpentine}}{\mathrm{Density} \mathrm{of} \mathrm{water}} \\ =\frac{840 \mathrm{kg}/{\mathrm{m}}^3}{1,000 \mathrm{kg}/{\mathrm{m}}^3} \\ =0.84 \end{gathered}$$

Ans: Relative density of turpentine = 0.84.

Answer:

(a) Pressure is defined as force per unit area applied in a direction perpendicular to the surface of an object.

(b) The relation between pressure, force, and area is given by following equation:
$\mathrm{Pressure}=\frac{\mathrm{Force}}{\mathrm{Area}}$
(c) (i) Area = 10 m²
Pressure = ?
Force = 200 N
$$\begin{gathered} \mathrm{Pressure}=\frac{\mathrm{Force}}{\mathrm{Area}} \\ =\frac{200}{10} \\ =20 \mathrm{Pa} \end{gathered}$$
Ans: Pressure = 20 Pa.

(ii) Area = 5 m²
Pressure = ?
Force = 200 N
$$\begin{gathered} \mathrm{Pressure}=\frac{\mathrm{Force}}{\mathrm{Area}} \\ =\frac{200}{5} \\ =40 \mathrm{Pa} \end{gathered}$$
Ans: Pressure = 40 Pa.

Answer:

(a) A substance which can flow is called fluid. The common fluids are juice, water, and soup.
(b) Archimedes’ principle states that “when a body is immersed partially or completely in a fluid (liquid or gas), it experiences an upthrust or buoyant force that is equal to the weight of the fluid displaced by body.”
(c) When an object is placed on the surface of water, two forces act on the object:
(i) The gravitational force that act in the downward direction.
(ii) The upthrust or the buoyant force that act in the upward direction.
An object floats on the surface of water if the upthrust of water on the object is greater than the weight of the object. An object sinks if the weight of the object is greater than the upthrust of water on the object.

Answer:

(a) The boat floats in water because the upthrust of water on the boat is greater than the weight of the boat.

(b) (i) ρ (density of steel piece) = ?
V (volume of steel piece) = 12 cm³
m (mass of steel piece) = 96 g
$$\begin{gathered} \mathrm{\rho }=\frac{m}{V} \\ =\frac{96}{12} \end{gathered}$$
ρ = 8 g/cm³
Ans: Density of steel piece = 8 g/cm³.

(ii) We know that 1 g/cm³ = 1,000 kg/m³
So, 8 g/cm³ = 8 × 1,000 kg/m³
                   = 8,000 kg/m³
Ans: Density of steel piece = 8,000 kg/m³.

Answer:

a) Elephant has larger weight of 40,000 N, so elephant exerts larger force on the ground. Elephant exerts a large force on the ground by 40,000 N − 400 N= 39,600 N.
b) Area of elephant’s one foot = 1,000 cm² (1,000/10,000= 0.1m²)
Pressure = ?
Weight of the elephant = 40,000 N
$$\begin{gathered} \mathrm{Pressure}=\frac{\mathrm{Weight}}{\mathrm{Area}} \\ =\frac{40,000}{0.1} \\ =4\times {10}^5\mathrm{Pa} \end{gathered}$$

Answer: Pressure exerted by one foot of elephant on the ground = 4 × 10⁵ Pa.
c) Area of one stiletto foot = 1 cm² = 0.0001 m²
Pressure = ?
Weight of the girl = 400 N
$$\begin{gathered} \mathrm{Pressure}=\frac{\mathrm{Weight}}{\mathrm{Area}} \\ =\frac{400}{0.0001} \\ =4\times {10}^6\mathrm{Pa} \end{gathered}$$
Answer: Pressure exerted by one foot of stiletto heel on the ground = 4 × 10⁶ Pa.

d) The girl standing on stiletto heel would exert larger pressure on the ground because the surface area covered by the heel is small as pressure is inversely proportional to the surface area of the heel.
e)  40,00,000 : 4,00,000 = 10:1
The pressure exerted by the girl is 10 times greater than the elephant.

Answer:

Ans: (a) 2N.
We know,
Buoyant force or weight of liquid displaced = Actual weight – Apparent weight
⇒ Weight of the liquid displaced = 10 – 8 = 2 N.

Answer:

Ans: c  The maximum pressure is exerted when breadth and height form the base.
This is because the pressure is inversely proportional to the surface area.

Answer:

Ans: c  d₁<d₂<d₃.
This is because if the density of the liquid is more than the object, then the object will float on the liquid. The more the object gets immersed in the liquid, lesser is the density of the liquid.

Answer:

Ans: c Mercury.
This is because the density of mercury is greater than the iron.

Answer:

Ans: b B.
This is because B has displaced maximum amount of water.

Answer:

Ans: c  R.
This is because R has the lowest density among the four.

Answer:

Ans: c  950.
The solid object floats in oil because the density of the solid object is less than the oil. The oil floats in water because the density of oil is less than water. Thus, the density of oil must be between density of solid and water.

Answer:

Ans: b.
$\mathrm{Density}=\frac{\mathrm{The} \mathrm{volume} \mathrm{of} \mathrm{a} \mathrm{certain} \mathrm{mass} \mathrm{of} \mathrm{copper}}{\mathrm{The} \mathrm{volume} \mathrm{of} \mathrm{the} \mathrm{same} \mathrm{mass} \mathrm{of} \mathrm{water}}=8.9$
This is because the density is defined as the ratio of the mass of the object to the volume of the object.

Answer:

Ans: d  X and Z.
This is because the density of these two liquids is same.

Answer:

Ans: d  D.
This is because among these four objects, only the density of object D is less than water.

Answer:

The two equal weights of unequal volumes will get unbalanced when they are completely immersed in water due to their unequal volumes; they will displace unequal volumes of water and will suffer unequal losses in weight when completely dipped in water.

Answer:

No, it is not necessary that their weights in air should also be the same. This is because the two bodies have undergone the same amount of loss in weight on completely immersing them in water due to their equal volumes and not because of their weights, so they may have different weights in air.

Answer:

The body will sink less in water because the density of water (1,000 kg/m3) is more than the density of kerosene (800 kg/m³).

Answer:

The reading on the spring balance will be zero. It is because the weight of floating block of wood is fully supported by the liquid in which it is floating. Hence, it does not exert any force on the spring balance.

Answer:

When a large amount of salt is dissolved in water, the density of salt solution becomes higher than pure water. It is because of its higher density, the salt solution exerts a greater upward buoyant force on the egg, making it rise and then float.

Answer:

(a) The beaker is suspended from a spring balance. If an object is added to the beaker, the net weight held by the spring balance increases. Thus, the reading of the spring balance will increase by the weight of the cork.

(b) The beaker is suspended from a spring balance. If an object is added to the beaker, the net weight held by the spring balance increases. Thus, the reading of the spring balance will increase by the weight of the heavy metal.

Answer:

ρ (density of golf ball) = ?
V (volume of steel piece) = 30 cm³
m (mass of steel piece) = 33 g
$$\begin{gathered} \mathrm{\rho }=\frac{m}{V} \\ =\frac{33}{30} \end{gathered}$$
ρ = 1.1 g/cm³
Ans: Density of the golf ball = 1.1 g/cm³.

Answer:

(a) The boat sinks a little more in water so that the weight of new volume of water displaced by the boat equalizes the weight of the boat and the boy.
(b) The weight of the water displaced by submerged part of the boat increases. It is now equal to sum of weight of boy and weight of boat.
(c) The buoyant force acting on the boat increases. The new buoyant force is equal to sum of weight of boy and weight of boat.

Answer:

A tin sheet sinks in water because the density of tin is higher than water. But the tin box or boat floats on water because of the trapping of large amount of air, whereby the average density of tin box or boat becomes lower than water.