Class 9 - foundation physics (Gravitation)

Two bodies of different masses are placed at a distance, if the distance is increased by 10%, then find the percentage change in gravitational force between the bodies.

Two person having mass 50 kg each, are standing such that the centre gravity are 1 m apart. Calculate the force of gravitation and also calculate the force of gravity on each. (Take $G = 6.67 \times 10^{- 11}$ $N m^{2} k g^{- 2}$ , mass of earth M = $6 \times 10^{24}$ kg, radius of earth R = $6.4 \times 10^{6} m$ ).

What is the gravitational attraction between a 70 kg boy and a 60 kg girl who are 3 meters apart?

If the radius of the earth were to shrink by one per cent, its mass remaining the same, the value of g on the earth's surface would
(1) increase by 0.5%
(2) increase by 2%
(3) decrease by 0.5%
(4) decrease by 2%

What will be the value of g at the bottom of sea 7 km deep? Diameter of Earth is 12800 km and g on the surface of Earth is 9.8 $m s^{- 2}$ .

An aeroplane flying horizontally at an altitiude of 2 km with a speed of 288 km/h. When it is just above a target it drops a bomb find by what distance, the bomb will miss the target and the time taken by it to hit the ground (Take g= 10 m/s).

Two masses 90 kg and 160 kg are at a distance 5 m apart. Compute the magnitude of intensity of the gravitational field at a point distance 3 m from the 90 kg and 4 m from the 160 kg mass. G = 6.67 $\times 10^{- 11} N m^{2} k g^{- 2}$ .

Find the potential energy of gravitational interaction of a point mass m and a thin uniform rod of mass M and length l, if they are located along a straight line at a distance a from each other.

Two thin rings each of radius R are coaxially placed at a distance R. The rings have a uniform mass distribution and have mass $m_{1}$ and $m_{2}$ respectively. Then the work done in moving a mass m from centre of one ring to that of the other is
(1) zero
(2) $\frac{G m (m_{1} - m_{2}) (\sqrt{2} - 1)}{\sqrt{2} R}$
(3) $\frac{G m (\sqrt{2}) (m_{1} - m_{2})}{R}$
(4) $\frac{G m m_{1} (\sqrt{2} + 1)}{m_{2} R}$

10.

Find the gravitational potential energy of a system of four particles, each having mass m, placed at the verticesof a square of side l. Also obtain the gravitational potential at the centre of the square.

11.

Determinethe the escape velocity of a body from the Moon. Take the Moon to be a uniform sphere of radius 1.74 $\times 10^{6}$ m and mass 7.39 $\times 10^{22} k g .$ Does your answer throws light on why the Moon has no atmosphere?

12.

Mass of moon is 1/81 times that of earth and its radius is 1/4 the earth's radius. If escape velocity at surface of earth is 11.2 km/se?c, then what is its value at the surface of the moon

13.

The planet Neptune travels around the Sun with a period of 165 years. Show that the radius of its orbit is approximately thirty that of Earth's orbit, both being considered as circular.

14.

Suppose Earth's orbital motion around the Sun is suddenly stopped. What time will the Earth take to fall into the sun?

15.

Two satellites have their masses in the ratio of 3 : 1. The radii of their circular orbits are in the ratio1 : 4. What is the ratio of total mechanical energy of A and B?

16.

Consider an Earth satellite so positioned that it appears stationary to an observer on Earth and serves the purpose of a fixed relay station for intercontinental transmission of TV and other communications. What would be the height at which the satellite should be positioned and what would be the direction of its motion? Given that the radius of the earth is 6400 km and acceleration due to gravity on the surface of the earth is 9.8 $m / s^{2} .$

17.

Two bodies A and B of masses m and 2m respectively are kept a distance d apart. Where should a small particle be placed, so that the net gravitation force on it due to the bodies A and B is zero?

18.

A body has a weight W on the surface of earth. What is its weight on a planet which has mass 10 times that of the Earth and a radius of 4 times that of the Earth?

19.

Calculate the value of acceleration due to gravity on the surface of the Moon.
(Given: Mass of the moon = 7.4 $\times 10^{22} k g$ , radius of moon=1740m, G=6.7 $\times 10^{- 11} N m^{2} / k g^{2}$ )

20.

a particle is taken to a height of 2 $R_{e}$ above the earth's surface, where $R_{e}$ is the radius of the Earth. If it is dropped from this height, what would be its acceleration?

21.

Two satellites A and B of equal mass move in the equatorial plane of the earth, close to earth's surface. Satellite A moves in the direction as that of the rotation of the Earth, while satellite B moves in the opposite direction. Calculate the ratio of the kinetic energy of B to that of A in the reference frame to the earth (Take g=9.8 m $s^{- 2}$ and radius of the Earth=6.37 $\times 10^{6}$ km).

22.

Determine the escape velocity of a body from the Moon. Take the moon to be a uniform sphere of radius 1.76 $\times 10^{6}$ m, and mass 7.36 $\times 10^{22}$ kg. Given G=6.67 $\times 10^{- 11} N m^{2} k g^{- 2}$ .

23.

Calculate the escape velocity for an atmospheric particle 1600 km above the Earth's surface, given that the radius of the Earth is 6400 km and acceleration due to gravity on the surface of earth is 9.8 m $s^{- 2}$ .

24.

State the universal law of gravitation.

25.

Write the formula to find the magnitude of gravitational force between the Earth and an object on the surface of the Earth.

26.

What do you mean by free fall?

27.

What do you mean by acceleration due to gravity?

28.

What are the differences between the mass of an object and its weight?

29.

Why is the weight of an object on the moon $\frac{1}{6}$ th its weight on the Earth?

30.

How does the force of gravitation between two objects change when the distance between them is reduced to half?

31.

Gravitational force acts on all object does not fall faster than a light object?

32.

What is the magnitude of the gravitational force between the Earth and a 1 kg object on its surface? (Mass of the Earth = $6 \times 10^{24}$ kg and radius of the Earth = $6.4 \times 10^{6}$ m)

33.

The Earth and the Moon are attracted to each other by gravitational force. Does the Earth attract the Moon with a force that is greater or smaller or the same as the force with which the Moon attracts the Earth? Why?

34.

If the Moon attracts the Earth, why does the earth not move towards the Moon?

35.

What happens to the force between two objects, if
(i) The mass of one object is doubled?
(ii) The distance between the object is doubled and tripled?
(iii) The masses of both objects are doubled?

36.

What is the importance of universal law of gravitation?

37.

What is the acceleration of free fall?

38.

What do we call the gravitational force between the Earth and an object?

39.

Amit buys few grams of gold at the poles as per the istruction of one of his friends. He hands over the same when he meets him at the equator. Will the friend agree with the weight of gold bought? If not, why? (Hint: The value of g is greater at the poles than at the equator).

40.

Why does a sheet of paper fall slower than one that is crumpled into a ball?

41.

Gravitational force on the surface of the Moon is only $\frac{1}{6}$ as strong as gravitational force on the Earth. What is the weight in newtons of a 10 kg object on the Moon and on the Earth?

42.

A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate
(i) The maximum height to which it rises,
(ii) The total time it takes to return to the surface of the Earth.

43.

A stone is released from the top of a tower of height 19.6 m. Calculate its final velocity just before touching the ground.

44.

A stone is thrown vertically upward with an initial velocity of 40 m/s. Taking g = 10 m/ $s^{2}$ , find the maximum height reached by the stone. What is th enet displacement and the total distance covered by the stone?

45.

Calculate the force of gravitation between the Earth and the Sun, given that the mass of the Earth = $6 \times 10^{24}$ kg and of the
Sun = $2 \times 10^{30}$ kg. The average distance between the two is 1.5 $\times 10^{11}$ m.

46.

A stone is allowed to fall from the top of a tower 100 m high and at the same time another stone is projected vertically upwards from the ground with a velocity of 25 m/s. Calculater when and where the two stones will meet?

47.

A ball thrown up vertically returns to the thrower after 6 s. Find
(a) The velocity wiht which it was thrown up
(b) The maximum height it reaches
(c) Its position after 4s.

48.

What is the source of centripetal force that a planet requires to revolve around the Sun? On what factors does that force depend?

49.

Suppose gravity of Earth suddenly becomes zero, then in which direction will the Moon begin to move if no other celestial affects it?

50.

Identical packets are dropped from two aeroplanes, one above the equator and the other above the north pole, both at height h. Assuming all conditions are identical, will those packets take same time to reach the surface of Earth. Justify your answer.

51.

The weight of any person on the Moon is about 1/6 times that on the Earth. He can lift a mass of 1.5 kg on the earth. What will be the maximum mass, which can be lifted by the same force applied by the person on the Moon?

52.

How does the weight of an object vary with respect to mass and radius of the Earth. If the diameter of the Earth becomes half of its present value and its mass becomes four times of its present value, then how would the weight of any object on the surface of the Eart be affected?

53.

Gravitational force acts on all bodies in proportion to their masses. Why, then, doesn't a heavy body fall faster than a light body?

54.

If the Earth were somehow expanded to a larger radius, with no change in mass, how would your weight be affected? How would it be affected if the Earth were shrunk instead?

55.

The figure shows four arrangements of three particles of equal masses. (a) Rank the arrangements according to the magnitude of the net gravitational force on the particle labeled m, greates first. (b) In arrangement 2, is the direction of the net force, closer to the line of length d or to the line of length D?
(1)

(2)

(3)

(4)

56.

If there is an attractive force between all objects, why do we not feel ourselves gravitating toward massive buildings in our vicinity?

57.

In what sense is drifting in space far away from all celestial bodies like stepping off a chair?

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