1.

Which of the following options are correct?

a)

Acceleration due to gravity decreases with increasing altitude.

b)

Acceleration due to gravity increases with increasing depth

c)

Acceleration due to gravity decreases with increasing depth

d)

Acceleration due to gravity is independent of the mass of the

planet

e)

g =0 at the center of the earth

(assume the earth to be a sphere of uniform density).

2.

Expression for gravitational force between two point masses m₁ & m₂ placed at a distance d between their centers is

a)

$F\ =\frac{Gm_1m_2}{d^2}$

b)

$F\ =\frac{Gm_1m_2}{d}$

c)

always attractive

d)

can be attractive or repulsive

3.

Gravitational force is

a)

conservative force

b)

long range force

c)

independent of the nature of the medium between the masses

d)

act along the line joining the centers of the two masses

e)

non conservative force

4.

Acceleration due to gravity (g) experienced by a mass (m) on a planet of mass M and radius R is

a)

$g\ =\frac{GM}{R^2}$

b)

$g\ =\frac{Gm}{R^2}$

c)

$g\ =\frac{GMm}{R^2}$

d)

$g\ =\frac{GM}{R}$

5.

If two masses m and M are placed at a distance apart , a point where the total gravitational force of these two on a third mass will be zero at a point

a)

Outside the line joining m & M but close to m

b)

Outside the line joining m & M but close to M

c)

In between the line joining m & M but close to m

d)

In between the line joining m & M but close to M

6.

If two masses m and M are placed at a distance d apart , a point where the total gravitational force of these two on a third mass will be zero at a point ( x is measured from the position of M )

a)

$x\ =\frac{d\sqrt[]{M}}{\left(\sqrt[]{M}+\sqrt[]{m}\right)}$

b)

Outsid $x\ =\frac{d\sqrt[]{M}}{\left(\sqrt[]{M}-\sqrt[]{m}\right)}$ e the line joining m & M but close to M

c)

In betw $x\ =\frac{d\sqrt[]{m}}{\left(\sqrt[]{M}+\sqrt[]{m}\right)}$ een the line joining m & M but close to m

d)

In bet $x\ =\frac{d\sqrt[]{m}}{\left(\sqrt[]{M}-\sqrt[]{m}\right)}$ ween the line joining m & M but close to M

7.

A point mass m is placed at a distance r from the center of a uniform spherical shell of mass M. Force (F) on m due to M is

a)

F = 0, if r < R

(any point inside M)

b)

F = 0, only if r = 0

( m palced at the center of M)

c)

F = 0, if r > R

d)

$F\ =\ \frac{GMm}{r^2}$ if r > R

e)

$F\ =\ \frac{GMm}{R^2}$ if r = R

8.

A mass m is taken from the surface of earth ( mass M & radius R) to a height h

a)

$g_h=g_s\ \left(1-\frac{2h}{R}\right)$ if h <<< R

b)

$\frac{g_h}{g_s}=\left(\frac{R}{R+h}\right)^2$ for all values of h

c)

$\frac{g_h}{g_s}=\left(\frac{R}{R-h}\right)^2$ for all values of h

d)

$\frac{g_h}{g_s}=\left(\frac{R+h}{R}\right)^2$ for all values of h

e)

$g_h=g_s\ \left(1+\frac{2h}{R}\right)$ if h <<< R

9.

A mass m is taken from the surface of earth ( mass M & radius R) to a height h

a)

$g_d=g_s\ \left(1_{ }+\frac{d}{R}\right)$

b)

$\frac{g_h}{g_s}=\left(\frac{R}{R-d}\right)^2$

c)

$\frac{g_h}{g_s}=\left(\frac{R}{R-h}\right)^2$

d)

$\frac{g_h}{g_s}=\left(\frac{R+d}{R}\right)^2$

e)

$g_h=g_s\ \left(1-\frac{d}{R}\right)$

10.

At what height from the surface of earth, is the value of g half that on the surface of earth? (R = radius of the earth)

a)

h = 0.414 R

b)

h = R

c)

h = 2 R

d)

h = 3.5 R

e)

h = R/2

11.

The value of g at a height of 100 km from the surface of the Earth is nearly (Radius of the Earth = 6400 km) (g on the surface of the Earth = 9.8 m/s²)

a)

9.8 m/s²

b)

9.5 m/s²

c)

10.5 m/s²

d)

9.0 m/s²

e)

0

12.

At what depth from the surface of earth, is the value of g half that on the surface of earth? (R = radius of the earth)

a)

$h\ =\frac{2R}{3}$

b)

h = R

c)

h = 2 R

d)

h = 3.5 R

e)

$h\ =\frac{R}{2}$

13.

At what height from the surface of earth the acceleration due to gravity will be reduced by 36 % its value o the surface of the earth?

a)

h = 4 R

b)

h = R

c)

h = 2 R

d)

h = R/4

e)

h = R/2

14.

Find the weight of an object at a height 6400 km above the earth's surface. The weight of the object at the surface of the earth is 20 N and the radius of the earth is 6,400 km.

a)

W = 0

b)

W = 5 N

c)

W = 10 N

d)

W = 4 N

e)

W = 20 N

15.

At what height from the surface of earth the acceleration due to gravity will be 36 % its value o the surface of the earth?

a)

h = 2R/3

b)

h = R

c)

h = 2 R

d)

h = R/4

e)

h = R/2

16.

ASSERTION (A) : Acceleration due to gravity near the pole more than that at the equator.

REASON (R) : Radius of the earth to the poles < radius of the earth to the equator

a)

Both A & R are true and R is the correct explanation for A

b)

Both A & R are true, but R is not the correct explanation for A

c)

A is true but R is false

d)

A is false but R is true

e)

Both A and R are false

17.

ASSERTION (A) : Escape speed from a planet increases if the mass and radius of the planet is doubled.

REASON (R) : Escape speed from a planet is directly proportional to mass of the planet inversely proportional to radius of the planet

a)

Both A & R are true and R is the correct explanation for A

b)

Both A & R are true, but R is not the correct explanation for A

c)

A is true but R is false

d)

A is false but R is true

e)

Both A and R are false

18.

ASSERTION (A) : Acceleration due to gravity deceases with increase in height from the surface of the earth and increases with increase in depth from the surface

REASON (R) : Acceleration due to gravity is directly proportional to depth and inversely proportional height and increases with increase in depth

a)

Both A & R are true and R is the correct explanation for A

b)

Both A & R are true, but R is not the correct explanation for A

c)

A is true but R is false

d)

A is false but R is true

e)

Both A and R are false

19.

ASSERTION (A) : Acceleration due to gravity on a 4 kg mass falling towards earth is double the acceleration due to gravity on a 2 kg mass falling towards earth.

REASON (R) : Acceleration due to gravity is directly proportional to mass of the object falling downwards

a)

Both A & R are true and R is the correct explanation for A

b)

Both A & R are true, but R is not the correct explanation for A

c)

A is true but R is false

d)

A is false but R is true

e)

Both A and R are false

20.

ASSERTION (A) : Escape speed for a 4 kg shot put from the surface of earth is twice the escape speed of a 1 kg shot put.

REASON (R) : Escape speed is directly proportional to the square root of mass of the object projected.

a)

Both A & R are true and R is the correct explanation for A

b)

Both A & R are true, but R is not the correct explanation for A

c)

A is true but R is false

d)

A is false but R is true

e)

Both A and R are false

21.

ASSERTION (A) : Work done by gravitational force is zero on a satellite revolving around the earth in circular orbit

REASON (R) : Gravitational force is a conservative force and work done by a conservative force is zero for a closed path.

a)

Both A & R are true and R is the correct explanation for A

b)

Both A & R are true, but R is not the correct explanation for A

c)

A is true but R is false

d)

A is false but R is true

e)

Both A and R are false

22.

ASSERTION (A) : Time period of a 400 kg satellite around earth is half the time period of a 100 kg satellite (assuming circular orbits).

REASON (R) : Time period of a satellite is inversely proportional to the square root of mass of the satellite.

a)

Both A & R are true and R is the correct explanation for A

b)

Both A & R are true, but R is not the correct explanation for A

c)

A is true but R is false

d)

A is false but R is true

e)

Both A and R are false

23.

ASSERTION (A) : Orbital speed of a satellite is independent of the mass of the satellite but depends on the orbital radius.

REASON (R) : Orbital speed of a satellite is = $v\ =\sqrt[]{\frac{GM}{R+h}}$ . (M & R are mass and radius of the planet and h is the height of the satellite from the surface of earth

a)

Both A & R are true and R is the correct explanation for A

b)

Both A & R are true, but R is not the correct explanation for A

c)

A is true but R is false

d)

A is false but R is true

e)

Both A and R are false

24.

Gravitational potential energy of a mass m at a distance r from the center of another mass M is

a)

$U_{12}=\frac{GMm}{r}$

b)

$U_{12}=-\frac{GMm}{r}$

c)

$U_{12}=\frac{GMm}{r^2}$

d)

$U_{12}=-\frac{GMm}{r^2}$

25.

The work done to dissociate a system of two particles with masses m₁ and m₂ separated by a distance d is

a)

$W\ =-\frac{Gm_1m_2}{d}$

b)

$W\ =\frac{Gm_1m_2}{d}$

c)

$W\ =-\frac{Gm_1m_2}{d^2}$

d)

$W\ =\frac{Gm_1m_2}{d^2}$

e)

= negative gravitational Potential energy

26.

Work done to dissociate a three particle system is =

a)

$\frac{Gm_1m_2}{r_{12}}+\frac{Gm_1m_3}{r_{13}}+\frac{Gm_2m_3}{r_{23}}$

b)

$-\left(\frac{Gm_1m_2}{r_{12}}+\frac{Gm_1m_3}{r_{13}}+\frac{Gm_2m_3}{r_{23}}\right)$

c)

$\frac{Gm_1m_2}{r_{12}}+\frac{Gm_1m_3}{r_{13}}$

d)

$-\left(\frac{Gm_1m_2}{r_{12}}+\frac{Gm_1m_3}{r_{13}}-\right)$

27.

Three identical masses m each are placed at the corners of an equilateral triangle of side L. The work done to send these masses to infinite distance away from each other is

a)

$\frac{3Gm^2}{L}$

b)

$\frac{Gm^2}{L}$

c)

$\frac{6Gm^2}{L}$

d)

$-\frac{3Gm^2}{L}$

e)

$-\frac{Gm^2}{L}$

28.

Four identical masses m each are placed at the corners of a square of side L. The work done to send these masses to infinite distance away from each other is

a)

$\frac{4Gm^2}{L}$

b)

$5.414\frac{Gm^2}{L}$

c)

$\frac{6Gm^2}{L}$

d)

$-\frac{4Gm^2}{L}$

e)

$-\frac{Gm^2}{L}$

29.

Gravitational potential of a mass M at a distance r from its center is

a)

$-\frac{GM}{r}$

b)

scalar

c)

vector

d)

$\frac{GM}{r}$

e)

$-\frac{GMm}{r}$

30.

The escape speed (v_e) of an object of mass m from the surface of a planet ( of mass M and radius R and acceleration due to gravity g) is

a)

$v_e=\sqrt[]{2gR}$

b)

$v_e=\sqrt[]{\frac{2GM}{R}}$ $wewer$

c)

$v_e=\sqrt[]{\frac{2Gm}{R}}$

d)

$v_e=\sqrt[]{\frac{GM}{R}}$

31.

If an object is projected with an initial speed = N times the escape speed ( N > 1), at infinity ( far away from the planet)

a)

PE = 0

b)

kE = 0

c)

final velocity =

$\sqrt[]{\left(N^2-1\right)}\times v_e$

d)

final velocity =

$\left(N^2-1\right)\times v_e$

32.

If an object is projected with an initial speed = $\frac{1}{N}$ times the escape speed from the surface of the earth of radius R ( N > 1), find the maximum height reached before returning

a)

$h\ =\frac{R}{N}$

b)

$h=\frac{R}{\ N\ -1}$

c)

$h=\frac{R}{\left(N^2-1\right)}$

d)

$h=\frac{R}{\left(\sqrt[]{N^2-1}\right)}$

33.

If an object is projected with an initial speed half of the escape speed from the surface of the earth of radius R , find the maximum height reached before returning

a)

$h\ =\frac{R}{2}$

b)

$h=R$

c)

$h=\frac{R}{3}$

d)

$h=\frac{R}{\left(\sqrt[]{3}\right)}$

34.

If an object is projected with an initial speed three times the escape speed from the surface of the earth, at infinity ( far away from the planet)

a)

PE = 0

b)

kE = 0

c)

final velocity =

$\sqrt[]{8}\times Ve$

d)

final velocity =

$8\ Ve$

35.

The orbital speed of a satellite (Vo) of mass m at a distance h from the surface of a planet of mass M and radius R is

a)

$V_o=\sqrt[]{\frac{GM}{R+h}}$

b)

$V_o=\sqrt[]{\frac{Gm}{R+h}}$

c)

$V_o=\sqrt[]{\frac{GM}{R}}$

d)

$V_o=\sqrt[]{\frac{Gm}{R}}$

36.

The time period of a satellite (Vo) of mass m at a distance h from the surface of a planet of mass M and radius R is

a)

$T=2\pi\sqrt[]{\frac{\left(R+h\right)^3}{GM}}$

b)

$T=2\pi\sqrt[]{\frac{\left(R+h\right)}{GM}}$

c)

$T=2\pi\sqrt[]{\left(\frac{GM}{\left(R+h\right)^3}\right)}$

d)

$T\ =2\sqrt[]{\frac{R^3}{GM}}$

37.

A satellite of mass m orbits around a planet of mass M at a distance r (r = R+h ) from the center of the planet, then

a)

$KE\ =\frac{GMm}{2r}$

b)

$PE\ =-\frac{GMm}{r}$

c)

Total energy = $-\frac{GMm}{2r}$

d)

Total energy = $\frac{GMm}{r}$

38.

A satellite of mass m orbits around a planet of mass M at a distance r (r = R+h ) from the center of the planet, then

a)

KE = - Total energy

b)

PE= 2 x Total energy

c)

PE= -2 x KE

d)

PE = 2 x KE

39.

A satellite of mass m is orbiting around a planet of mass M at a distance a from the center of the planet. Find the work done to shift the satellite to a new orbit of radius b ( b > a)

a)

$W\ =\ \frac{GMm}{2}\left(\frac{1}{a}-\frac{1}{b}\right)$

b)

$W\ =\ \frac{GMm}{2}\left(\frac{1}{b}-\frac{1}{a}\right)$

c)

$W\ =\ GMm\left(\frac{1}{a}-\frac{1}{b}\right)$

d)

$W\ =\ GMm\left(\frac{1}{b}-\frac{1}{a}\right)$

40.

The work done to increase the radius of orbit of a satellite of mass m revolving around a planet of mass M from orbit of radius R into another orbit of radius 3R is

a)

$W\ =\ \frac{2gmR}{3}$

b)

$W\ =\ \frac{gmR}{3}$

c)

$W=\frac{2}{3}gMR$

d)

$W\ =\frac{3}{2}gmR$

41.

Three identical masses m each are placed at the corners of an equilateral triangle of side a. What is the net force on a fourth identical mass placed at the center of the triangle ?

a)

F = 0

b)

$F\ =\ \frac{3Gm^2}{a}$

c)

$F\ =\ \frac{Gm^2}{a}$

d)

$F\ =\sqrt[]{3}\ \frac{Gm^2}{a}$

42.

The value of g at a particular point on the surface of earth is 9.8 m/s² Suppose the earth suddenly shrink uniformly to half its present size without losing any mass. The value of g at the same point (assuming that the distance of the point from the center of the earth does not shrink) is

a)

9.8 m/s²

b)

4.9 m/s²

c)

19.6 m/s²

d)

2.45 m/s²

43.

The figure shows the elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded area SAB. If t₁ is the time for the planet to move from C to D and t₂ is the time to move from A to B then

a)

$t_1=2t_2$

b)

$t_2=2t_1$

c)

$t_1=4t_2$

d)

$t_2=4t_1$

44.

The mass of the moon is 1% of mass of the earth. The ratio of gravitational pull of earth on moon to that of moon on earth will be:

a)

1 : 1

b)

1 : 10

c)

1 : 100

d)

100 : 1

45.

At what distance (in meter) from the center of the Moon, the intensity of gravitational field will be zero? (Take mass of Earth is 81 times the mass of moon respectively and the distance between Moon and Earth is 3.85 × 10⁸ m)

a)

3. 9 × 10⁶

b)

0.39 × 10⁸

c)

8 × 10⁸

d)

3.46 × 10⁸

46.

If the Earth losses its gravity, then for a body its mass and weight will be

a)

same and zero

b)

zero and same

c)

zero and zero

d)

two times and zero

47.

A point mass m is placed at a distance r = R/2 fro the center a uniform spherical shell of radius R and mass M. The gravitational force exerted by the shell on the point mass is

a)

$\frac{4GMm}{R^2}$

b)

$\frac{GMm}{R^2}$

c)

zero

d)

$\frac{2GMm}{R^2}$

48.

A point mass m is placed at a distance r = 2R fro the center a uniform spherical shell of radius R and mass M. The gravitational force exerted by the shell on the point mass is

a)

$\frac{4GMm}{R^2}$

b)

$\frac{GMm}{4R^2}$

c)

zero

d)

$\frac{GMm}{2R^2}$

49.

The acceleration due to gravity is g at a point distance r from the center of earth R. If r < R then

a)

$g\ \alpha\ r^2$

b)

$g\ \alpha\ r$

c)

$g\ \alpha\ r^{-2}$

d)

$g\ \alpha\ r^{-1}$

50.

The acceleration due to gravity is g at a point distance r from the center of earth R. If r > R then

a)

$g\ \alpha\ r^2$

b)

$g\ \alpha\ r$

c)

$g\ \alpha\ r^{-2}$

d)

$g\ \alpha\ r^{-1}$

51.

If R is the radius of the earth and g is the acceleration due to gravity on the earth's surface, then mean density of the earth is

a)

$\frac{3g}{4\pi RG}$

b)

$\frac{3G}{4\pi Rg}$

c)

$\frac{3g}{4\pi R^2G}$

d)

$\frac{3G}{4\pi R^2g}$

52.

The mass of earth is 80 times that of another planet and its diameter is double that of the planet. If the value of acceleration due to gravity on earth is 9.8 m/s², then the value of acceleration due to gravity on the planet will be

(a) 0.98 m/s² (b) 4.9 m/s²(c) 9.8 m/s² (d) 0.49 m/s²

a)

4.9 m/s²

b)

9.8 m/s

c)

0.49 m/s²

d)

0.98 m/s²

53.

Which of the following graphs shows an approximate variation of acceleration due to gravity g with height h above the Earth's surface?

a)

A

b)

B

c)

C

d)

D

54.

Which of the following graphs shows an approximate variation of acceleration due to gravity g with depth h below the Earth's surface?

a)

A

b)

B

c)

C

d)

D

55.

At what height above the earth’s surface would the acceleration due to gravity be one-fourth of its value at the earth’s surface?

a)

h = 4R

b)

h = 2R

c)

h = R

d)

h = 16R

56.

At what height h above earth, the value of g becomes g/2? (R = Radius of earth)

a)

$\left(\sqrt[]{2}+1\right)R$

b)

$\sqrt[]{2}R$

c)

$\frac{R}{\sqrt[]{2}}$

d)

$\left(\sqrt[]{2}-1\right)R$

57.

The ratio of the acceleration due to gravity as the bottom of a deep mine and that on the surface of the earth is 978/980. Find the depth of the mine, if the density of the earth is uniform throughout and the radius of the earth is 6300 km.

a)

13 km

b)

90 km

c)

25 km

d)

26 km

58.

A ball is dropped from a spacecraft revolving around the earth at height of 120km. What will happen to ball ?

a)

It will continue to move with the same speed along the original orbit of spacecraft

b)

It will move the same speed, tangentially to the spacecraft

c)

It will fall down to the earth gradually

d)

It will go very far in space

59.

The velocity with which a projectile must be fired so that it escapes earth's gravitation does not depend on

a)

Mass of the earth

b)

radius of the projectile’s orbit

c)

Mass of the projectile

d)

Gravitational constan

60.

The escape velocity for a body projected vertically upwards from the surface of earth is approximately 11 km/s. If the body is projected at an angle of 45⁰ with the vertical, the escape velocity will be

a)

11 km/s

b)

$11\ \sqrt[]{2}$ km/s

c)

$\frac{11}{\sqrt[]{2}}$ km/s

d)

22 km/s

61.

The escape velocity from the earth is 11.2 km/s, the mass of another planet is 1000 times of mass of earth and its radius is 10 times the radius of earth. The escape velocity for the planet is

a)

11200 km/s

b)

11.2 km/s

c)

112 km/s

d)

56 km/s

62.

The mass of the moon is 1/81 of earth's mass and its radius 1/4 that of the earth. If the escape velocity from the earth's surface is 11.2 km/sec. its value from the surface of the moon will be

a)

5.0 km/s

b)

0.14 km/s

c)

2.5 km/s

d)

0.5 km/s

63.

The minimum energy required to take a m kg satellite from earth's surface in a circular orbit at a height of 2R from the surface of earth where R is the radius of earth, will be:

a)

$\frac{5}{6}mgR$

b)

$\frac{6}{5}mgR$

c)

$\frac{5}{12}mgR$

d)

$\frac{2}{3}mgR$

64.

If the orbital radius of the earth is made 4 times, then find the duration of the year if earlier it was T?

a)

T

b)

2T

c)

4T

d)

8T

65.

Two satellites of masses m₁ and m₂ (m₁>m₂) are revolving around the earth in a circular orbit of radii r₁ and r₂ (r₁> r₂), respectively. Which of the following statements is true regarding their speeds v₁ and v₂?

a)

v₁= v₂

b)

v_{1 >}v₂

c)

v_{1 <}v₂

d)

$v_1\le v_2$

GRAVITATION

Total questions: 65

Worksheet time: 42mins

At what height from the surface of earth, is the value of g half that on the surface of earth? (R = radius of the earth)

The value of g at a height of 100 km from the surface of the Earth is nearly (Radius of the Earth = 6400 km) (g on the surface of the Earth = 9.8 m/s²)

9.8 m/s²

9.5 m/s²

10.5 m/s²

9.0 m/s²

At what depth from the surface of earth, is the value of g half that on the surface of earth? (R = radius of the earth)

At what height from the surface of earth the acceleration due to gravity will be reduced by 36 % its value o the surface of the earth?

Find the weight of an object at a height 6400 km above the earth's surface. The weight of the object at the surface of the earth is 20 N and the radius of the earth is 6,400 km.

At what height from the surface of earth the acceleration due to gravity will be 36 % its value o the surface of the earth?

The work done to increase the radius of orbit of a satellite of mass m revolving around a planet of mass M from orbit of radius R into another orbit of radius 3R is

Which of the following graphs shows an approximate variation of acceleration due to gravity g with height h above the Earth's surface?

Which of the following graphs shows an approximate variation of acceleration due to gravity g with depth h below the Earth's surface?

Similar Resources on Wayground

GRAVITATION

Total questions: 65

Worksheet time: 42mins

At what height from the surface of earth, is the value of g half that on the surface of earth? (R = radius of the earth)

The value of g at a height of 100 km from the surface of the Earth is nearly (Radius of the Earth = 6400 km) (g on the surface of the Earth = 9.8 m/s2)

9.8 m/s2

9.5 m/s2

10.5 m/s2

9.0 m/s2

At what depth from the surface of earth, is the value of g half that on the surface of earth? (R = radius of the earth)

At what height from the surface of earth the acceleration due to gravity will be reduced by 36 % its value o the surface of the earth?

Find the weight of an object at a height 6400 km above the earth's surface. The weight of the object at the surface of the earth is 20 N and the radius of the earth is 6,400 km.

At what height from the surface of earth the acceleration due to gravity will be 36 % its value o the surface of the earth?

The work done to increase the radius of orbit of a satellite of mass m revolving around a planet of mass M from orbit of radius R into another orbit of radius 3R is

Which of the following graphs shows an approximate variation of acceleration due to gravity g with height h above the Earth's surface?

Which of the following graphs shows an approximate variation of acceleration due to gravity g with depth h below the Earth's surface?

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The value of g at a height of 100 km from the surface of the Earth is nearly (Radius of the Earth = 6400 km) (g on the surface of the Earth = 9.8 m/s²)

9.8 m/s²

9.5 m/s²

10.5 m/s²

9.0 m/s²