# Worksheets on gravity

Here is the collection of the objective questions related to the gravitation topic .You can check your answer on the bottom of the worksheet.

1>Newton’s law of gravitation gives

(1) gravitational force between earth and a point mass only

(2) gravitational force between sun and earth only

(3) electrical force between two charged particles only

(4) gravitational force between any two bodies placed at a sufficient distant apart

2>The value of g depends on

(1) mass of earth only

(3) mass and radius of earth both

(4) is a constant independent of mass and radius of earth

3>The value of G depends on

(1) mass of earth only

(3) mass and earth both

(4) is a constant independent of mass and radius of earth

4>The value of universal gravitational Constant G in S.I system is

(1) 9.8 m/s2

(2) $6.67 \times 10^{-7} N-m^2 /kg^2$

(3) ) $6.67 \times 10^{11} N-m^2 /kg^2$

(4) ) $6.67 \times 10^{-11} N-m^2 /kg^2$

5>The Force between two particles of masses m1 and m2 at separation r is given by

$F = \dfrac{G m_1 m_2}{r^2}$

From this  $G = \dfrac{F r^2}{m_1 m_2}$

If the masses of particles are doubled, keeping distance unchanged, the value of G would become/remain

(1) $\dfrac{1}{4}$ times

(2) 4 – times

(3) $\dfrac{1}{2}$ times

(4) Unchanged

6>If the distance between two point masses is doubled, the gravitational attraction between them

(1) is doubled

(2) becomes four times

(3) is reduced to half

(4) is reduced to a quarter

7>The atmosphere is held to the earth by

(1) gravity

(2) winds

(3) clouds

(4) rotation of earth around the sun

8>The value of universal gravitational constant depends on

(1) the nature and the size of bodies.

(2) the medium between the two masses

(3) the temperature of the bodies

(4) it is a universal constant and does not depend on conditions

9>The force of attraction between two unit point masses at a unit separation is called

(1) gravitational potential

(2) gravitational intensity

(3) acceleration due to gravity

(4) universal gravitational constant

10>Which of the following fundamental interactions is weakest ?

(1) nuclear

(2) electromagnetic

(3) gravitational

(4) all above are equally strong

11> The particle which is exchanged between the two bodies due to gravitational  force of attraction between them is called

(1) muon

(2) hyperon

(3) graviton

(4) photon

12>The gravitational potential due to the earth on its surface is

(1) negative

(2) zero

(3) positive

(4) infinity

13>The ratio of inertial mass to gravitational mass is

(1) 0.5

(2) 1

(3) 2 A

(4) 4

14>The weight of a body at the centre of earth is

(1) zero

(2) infinite

(3) slightly less than at the poles

(4) slightly less than at the equator

15>The mass of a particle at the centre of earth is

(1) zero

(2) infinite

(3) slightly more than at the poles

(4) same as at other places

16>The force of gravitational attraction on a body is

(1) minimum at the equator

(2) minimum at the poles

(3) minimum midway between poles and equator

(4) same at all points on earth’s surface

17>As we go from the equator to the poles, the value of g

(1) decreases

(2) increases

(3) decreases up to a latitude of 45°

(4) remain the same

18>All bodies large and small fall under gravity with same

(1) Force

(2) Velocity

(3) Acceleration

(4) Momentum

19>Consider the earth to be a homogeneous sphere. Scientist A goes deep down in a mine and Scientist B goes high up in the balloon. The gravitational field measured by

(1) A goes on decreasing and that by B goes on increasing

(2) B goes on decreasing and that goes on decreasing

(3) Each remains unchanged

(4) goes on decreasing

20>Consider the earth to be a homogeneous sphere Scientist A goes down 1 km in a mine and Scientist B goes up 1 km high mountain. The Scientists observe the values of g as gA and
gB respectively then,

(1) $g_A > g_B$

(2) $g_A < g_B$

(3)  $g_A = g_B$

(4) $g_A \geq g_B$

21>If g is acceleration due to gravity at earth’s surface, then the acceleration due to gravity at a
planet whose mass and radius are both half of that of the earth will be

(1) $\dfrac{g}{4}$

(2) $\dfrac{g}{2}$

(3) g

(4) 2g

22>If the speed of rotation of the earth increases, then the weight of the body

(1) increases

(2) decreases

(3) remains unchanged

(4) may increase or decrease

23>If the earth stops rotating about its axis, the value of g will

(1) increase

(2) decrease

(3) remain unchanged

(4) may increase or decrease

24>If the earth suddenly stops rotating about its axis, the value of g at the equator will

(1) decrease by ${\omega}^2 \, R$

(2) increase by  ${\omega}^2 \, R$

(3) increase by  $\omega \, R$

(4) remain unchanged

25>Weightlessness experienced while orbiting the earth in spaceship is the result of

(1) inertia

(2) acceleration

(3) zero gravity

(4) centre of gravity

26>The escape velocity of a particle of mass m varies as

(1) $m^2$

(2) m

(3) $m^0$

(4) $m^{-1}$

27>The escape velocity from the earth’s surface in km/sec is about

(1) 4.2

(2) 7.2

(3) 9.2

(4) 11.2

28>The first cosmic velocity is

(1) 5 km/s

(2) 8 km/s

(3) 11.2 km/s

(4) 17 km/s

29>The second cosmic velocity is

(1) 5 km/s

(2) 8 km/s

(3) 11.2 km/s

(4) 17 km/s

30>The third cosmic velocity is

(1) 5 km/s

(2) 8 km/s

(3) 11.2 km/s

(4) 17 km/s

31>The relation between escape velocity  $v_e$ and orbital velocity  $v_o$ is given by

(1) $v_e = \sqrt{2} v_o$

(2) $v_e = 2 v_o$

(3) $v_e = \dfrac{v_o}{\sqrt{2}}$

(4) $v_e = \dfrac{v_o}{2}$

32>The relation between orbital kinetic energy $E_o$ and escape kinetic energy  $E_e$ is given by

(1) $E_e = \sqrt{2} E_o$

(2) $E_e = 2 E_o$

(3) $E_e = \dfrac{E_o}{\sqrt{2}}$

(4) $E_e = \dfrac{E_o}{2}$

33> A satellite is orbiting close to earth’s surface, then its orbital speed is

(1) $\sqrt{2 Rg}$

(2) $\sqrt{Rg}$

(3) $\sqrt{\dfrac{Rg}{2}}$

(4) ${Rg}^2$

34>A satellite is orbiting close to earth’s surface, its time period is

(1) $\pi \sqrt{\dfrac{2 R}{g}}$

(2) $2 \pi \sqrt{\dfrac{R}{g}}$

(3) $2 \pi \sqrt{\dfrac{R}{2g}}$

(4) $\dfrac{\pi}{2} \sqrt{\dfrac{R}{g}}$

35>A man inside an artificial satellite feels weightlessness because the force of attraction due to earth is

(1) zero at that place

(2) is, balanced by the force of attraction due to moon

(3) is not effective due to design of satellite

(4) balanced by the centrifugal acceleration

36>The communication satellite may be installed

(1) over Delhi

(2) over Bombay

(3) over Chandigarh

(4) over equatorial plane

37>An astronaut orbiting the earth in a circular orbit 200 km above the surface of earth gently drops a packet out of the spaceship. It will

(1) move towards the moon

(2) fall vertically down to the earth

(3) move in a zigzag way and then fall to the earth

(4) move along with the spaceship

38>A satellite revolves around the earth in an elliptical orbit. Its speed

(1) is same at all points of the orbit

(2) is greatest when it is closest to earth

(3) is greatest when it is farthest to earth

(4) goes on decreasing or increasing continuously depending on the mass of the satellite

39> If the speed of a satellite moving near a planet in circular orbit is increased by 41.4%. It will

(1) fall into the planet

(2) move in an orbit of smaller radius

(3) move in an orbit of larger radius

(4) escape from the planet

40>The height of communication satellite from earth’s surface is

(1) 3600 km

(2) 6400 km

(3) 36000 km

(4) 42000 km

41>The time period of a geostationary satellite is

(1) one year

(2) one month

(3) one day

(4) depends on height above earth’s surface

42>If G is gravitational constant and R is the radius of earth, then acceleration due to gravity ‘g’ and the mean density of the earth (D) are related by the equation

(1) $D = \dfrac{g}{G} ( \dfrac{4}{3} \pi R^2 )$

(2) $D = \dfrac{( g/G )}{ \dfrac{4}{3} \pi R}$

(3) $D = ( \dfrac{g}{G} ) ( \dfrac{4}{3} \pi R^2 )$

(4) $D = \dfrac{( g/G )}{ \dfrac{4}{3} \pi R^3}$

43>The radius of the earth is about 6400 km and that of Mars is about 3200 km. The mass of earth is about 10 times the mass of the Mars. As object weights 200 N on earth’s surface, then its weight on the surface of the Mars would be

(1) 8 N

(2) 20 N

(3) 40 N

(4) 80 N

44>The escape velocity of a body on the surface of earth is 11.2 km/s. If the earth’s mass increases to twice its present value and the radius of earth becomes half, the escape velocity would become/remain

(1) 5.6 km/s

(2) 11.2 km/s

(3) 22.4 km/s

(4) 44.8 km/s

45>The escape velocity of a body from earth’s surface face when projected vertically is 11.2 km/s.
The escape velocity of the body when projected from earth’s surface at an angle 60° to the horizontal is

(1) 5.6 km/s

(2) $5.6 \sqrt{3} km/s$

(3) 11.2 km/s

(4) $11.2 \times \sqrt{3} km/s$

46>The escape velocity of a body of mass m from earth’s surface is 11.2 km/s. The escape velocity of a body of mass 2m from earth’s surface will be

(1) 5.6 km/s

(2) 11.2 km/s

(3) 22.4 km/s

(4) 44.8 km/s

47>The distance of two planets from the sun are $10^13$ m and $10^12$ m respectively. The ratio of the time periods of these planets will be

(1) $\dfrac{1}{\sqrt{10}}$

(2) 100

(3) $10 \sqrt{10}$

(4) $\sqrt{10}$

48>The earth (mass = $6 \times 10^24$ kg ) revolves around the sun with an angular velocity of $2 \times 10^{-7}$ radian/sec in a circular orbit of radius $1.5 \times 10^8$ km. The force exerted by the sun on earth in Newton is

(1) zero

(2) $36 \times 10^21$

(3) $18 \times 10^25$

(4) $1.5 \times 10^8$

49>A satellite A of mass m is at a distance r from the centre of the earth. Another satellite B of
mass 2m is at a distance 2r from earth’s centre. Their time periods are in the ratio of

(1) 1 : 2

(2) 1 : 16

(3) 1 : 32

(4) $1 : 2 \sqrt{2}$

50>What is the mass of the earth in terms of g, Re and G?

(1) $g^2 \dfrac{R_e}{G}$

(2) $G \dfrac{R_e^2}{g}$

(3) $G \dfrac{R_e}{g}$

(4) $g \dfrac{R_e^2}{G}$

51>Two types of balances the beam balance and the spring balance are commonly used for measuring weight in shops. If we are on moon, we can continue to use

(1) Only the beam type balance without any change

(2) Only the spring type balance without any change

(3) Both the balances without any change

(4) Neither of the two balances without making any change

52>Two types of clocks: pendulum clock and spring clock are available to record time on earth. Then if we are in a satellite, we can continue to use

(1) Only the spring clock

(2) Only the pendulum clock

(3) Both spring and pendulum clocks

(4) Neither spring clock nor pendulum clock

53>The mean radius of earth is R, its angular speed on its axis is $\omega$ and the acceleration due to gravity at earth’s surface is g. The cube of the radius of the orbit of a geostationary satellite will be

(1) $\dfrac{R^2 g}{\omega}$

(2) $\dfrac{R^2 {\omega}^2}{g}$

(3) $\dfrac{R g}{\omega}$

(4) $\dfrac{R^2 g}{{\omega}^2}$

54>The radius of earth is 6400 km and g = 10 m/s2. In order that a body of 5 kg weight zero at the equator, then the angular speed of the earth will be

(1) $\dfrac{1}{80}$ rad/s

(2) $\dfrac{1}{400}$ rad/s

(3) $\dfrac{1}{800}$ rad/s

(4) $\dfrac{1}{1600}$ rad/s

55>The escape speed for a projectile from earth’s surface is 11.2 km/s. A body is projected from earth’s surface with a speed equal to 4 times the escape speed. The speed the body when at infinite separation from the centre of the earth is

(1) $4 \times 11.2 \, km/s$

(2) $3 \times 11.2 \, km/s$

(3) $11.2 \times \sqrt{15} \, km/s$

(4)  Zero km/s

56>Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a time period T. If the gravitational force of attraction between the planet and the star be
proportional to $R ^{- \dfrac{5}{2}}$ , then T2 is proportional to

(1) $R^2$

(2) $R^{\dfrac{7}{2}}$

(3) $R^{\dfrac{5}{2}}$

(4) $R^3$

57>A planet moves around the sun in elliptical orbit. At a point P it is closest to sun at a distance d1 and has speed v1. At another point Q when it is farthest from the sun at a distance d2, its speed will be

(1) $\dfrac{{d_1}^2 v_1}{{d_2}^2}$

(2) $\dfrac{d_2 v_2}{d_1}$

(3) $\dfrac{d_1 v_1}{d_2}$

(4) $\dfrac{{d_2}^2 v_1}{{d_1}^2}$

58>The escape velocity from a spherical planet is ve. What is the escape velocity corresponding to another planet of twice the radius and half the mean density?

(1) $\sqrt{2} v_e$

(2) $\dfrac{v_e}{\sqrt{2}}$

(3) $2 v_e$

(4) $4 v_e$

59>The ratio of the radius of earth to moon is 10. The ratio of acceleration due to gravity on earth and on the moon is 6. The ratio of the escape velocity from the earth’s surface to that from the moon is

(1) 1.65

(2) 6

(3) Nearly 8

(4) 10

60>Escape velocity of a body from earth is about 11 km/s. Assuming the mass and radius of earth to be about 81 and 4 times the mass and the radius of moon; the escape velocity in km/s from the surface of the moon will be

(1) 0.54

(2) 2.44

(3) 11

(4) 49.5

61>The value of ‘g’ at a particular point is 9.8 m/s2. Suppose the earth suddenly strikes to
one-third of its present size without losing any mass. The value of g at the same point (assuming that the distance of the point from the centre of earth remains unchanged) will now be

(1) $3.3 \, m/s^2$

(2) $9.8 \, m/s^2$

(3) $29.4 \, m/s^2$

(4) $88.2 \, m/s^2$

62>The value of ‘g’ at earth’s surface is 9.8 m/s2. Suppose the earth suddenly strikes to one-third of its present size without losing any mass. The value of g on the surface of this smaller earth will be

(1) $3.3 \, m/s^2$

(2) $9.8 \, m/s^2$

(3) $29.4 \, m/s^2$

(4) $88.2 \, m/s^2$

63>The value of g will be 1% of its value at the surface of earth at a height (radius of earth Re = 6400 km)

(1) 6400 km

(2) 2560 km

(3) 57600 km

(4) 64000 km

64>The change in the value of ‘g’ at a height ‘h’ above the surface of the earth is same at a depth x below it, then (assume both x and h much smaller than the radius of the earth)

(1) x = h

(2) x =2h

(3) $x= \dfrac{1}{2h}$

(4) $x = \dfrac{h}{2}$

65>For earth satellite in circular orbit, which of the following is correct?

(1) It is a freely falling body

(2) It is out of gravitational field

(3) Its linear momentum remains constant

(4) It possesses no acceleration

66>The mean distance of Jupiter from the sun is nearly 5.2 times the corresponding earth-sun distance. According to Kepler’s law the period of revolution of Jupiter in its orbit will be

(1) 5 years

(2) 7.5 years

(3) 12 years

(4) 25 years

67>Two planets are moving round the sun. Their mean orbital radii are r1 and r2. Then the ratio of their time period $\dfrac{T_1}{T_2}$ is equal to

(1) $( \dfrac{r_1}{r_2} )$

(2) $( \dfrac{r_1}{r_2} )^{\dfrac{3}{2}}$

(3) $( \dfrac{r_1}{r_2} )^3$

(4) $( \dfrac{r_2}{r_1} )^{\dfrac{3}{2}}$

68>Which of the followings graphs represent the relation of time period T of a planet moving about the sun in orbit of radius r

69>Kepler’s second law states that the straight line joining the planet to the sun sweeps equal areas in equal times. This statement is equivalent to saying that

(1) Acceleration of the planet is zero

(2) Transverse acceleration of the planet is zero

(3) Tangential acceleration of the planet is zero

(4) Radial acceleration of the planet is zero

(1) liquid fuel

(2) solar energy

(3) atomic energy

(4) no energy is needed

71>The binding energy of earth-satellite sy stem is (Me = mass of earth, Ms = mass of satellite,
r = distance of satellite from centre of earth)

(1) $- \dfrac{G M_e M_s}{r}$

(2)  $- \dfrac{G M_e M_s}{2r}$

(3) $\dfrac{G M_e M_s}{r}$

(4) $\dfrac{G M_e M_s}{2r}$

72>A satellite of mass m is orbiting around the earth in a circular orbit with speed v. The total energy of the satellite is

(1) $m v^2$

(2) $\dfrac{1}{2} m v^2$

(3) $\dfrac{3}{4} m v^2$

(4) $- \dfrac{1}{2} m v^2$

73>Two identical trains are moving on rails along the equator on the earth in opposite directions. The pressure exerted by the trains on the rails will be

(1) Zero

(2) Equal

(3) Unequal

(4) Uncertain

74>A helium balloon released on moon would

(1) climb with an acceleration $\dfrac{9.8}{5} m/s^2$

(2) fall with an acceleration $\dfrac{9.8}{6} m/s^2$

(3) climb with an acceleration $9.8 \times 6 m/s^2$

(4) remain stationary wherever left

75>A planet is moving in an elliptical orbit. If T, V, E, $\overrightarrow{L}$ stand respectively for its kinetic energy, gravitational potential energy, total energy, angular momentum about the centre of force, which of the following statements is correct ?

(1) T is conserved

(2) V is always positive

(3) is always negative

(4) $\overrightarrow{L}$ is constant in magnitude but its direction changes continuously

76>The given fig. shows the motion of the planet around the sun S in an elliptical orbit with the sun at the focus. The shaded area A and B are also shown in fig. which can be assumed to be equal. If t1 and t2 represent the times taken for the planet to move from a to b and from c to d respectively, then

(1) $t_1 < t_2$

(2) $t_1 > t_2$

(3) $t_1 = t_2$

(4) $t_1 \, \text{and} \, t_2$ cannot be compared

77>The weight of a body at a height equal to the radius of earth is W. Its weight at a height equal to three times the radius of earth will be

(1) $\dfrac{W}{4}$

(2) $\dfrac{W}{3}$

(3) $\dfrac{W}{2}$

(4) $\dfrac{2}{3} W$

78>Three identical bodies each of mass M move in a circle of radius R under the action of their gravitational attraction. The speed of each body is

(1) $\sqrt{\dfrac{GM}{R}}$

(2) $\sqrt{\dfrac{GM}{3R}}$

(3) $\sqrt{\dfrac{GM}{\sqrt{3}R}}$

(4) $\sqrt{\dfrac{GM}{\sqrt{2}R}}$

79>An unmanned space probe is to be thrown with such a velocity that it does not return to earth. It would be thrown with

(1) Only the velocity  $\sqrt{\dfrac{2GM}{R}}$

(2) Velocity > $\sqrt{\dfrac{2GM}{R}}$ necessarily

(3) Velocity $\geq \sqrt{\dfrac{2GM}{R}}$

(4) A great velocity but nothing more can be said about

80>A satellite which is geostationary in a particular orbit is taken to another orbit, the distance of which is twice that of earlier orbit. The time period of the satellite in second orbit will be

(1) 24 h

(2) 48 h

(3) $48 \sqrt{2} h$

(4) $24 \sqrt{2}$

81.Two satellites S1 and S2 revolve around the earth at distances 3R and 6R from the centre of earth. Their periods of revolutions will be in the ratio

(1) 1 : 2

(2) 2 : 1

(3) $1 : 2^{1.5}$

(4) $1 : 2^{0.67}$

82> The escape velocity for the moon is nearly

(1) 11.2 km/s

(2) 24 km/s

(3) 8 km/s

(4) 2.4 km/s

83>The gravitational potential at a height h above the earth’s surface is $5.12 \times 10^{27}$ J/kg and the value of g at this point is 6.4 ms-2. If the radius of the earth be 6400 km, the value of h is

(1) 1200 km

(2) 1600 km

(3) 1800 km

(4) 2400 km

84>A metal ball and an air bubble in water

(1) attract each other

(2) repel each other

(3) do no interact with each other

(4) attract at poles and repel at equator