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Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is :

(A)

7.5 R

(B)

1.5 R

(C)

2.5 R

(D)

4.5 R

Question-2

Suppose the gravitational force varies inversely as the n^{th} power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to :

(A)

R^{n}

(B)

(C)

(D)

Question-3

The kinetic energy needed to project a body of mass m from the earth's surface (radius R) to infinity is :

(A)

mgR

(B)

(C)

(D)

2mgR

Question-4

Energy required to move a body of mass m from an orbit of radius 2R to 3R is :

(A)

(B)

(C)

(D)

Question-5

The weight of a body at earth surface is 700 g wt. What will be its weight on a planet whose mass is 1/7 that of earth and radius half that of earth?

(A)

300 g-wt

(B)

200 g-wt

(C)

400 g-wt

(D)

57.1 g-wt

Question-6

If the radius of the earth decreases by 10%, the mass remaining unchanged, what will happen to the acceleration due to gravity?

(A)

Decreases by 19%

(B)

Increases by 19%

(C)

Decreases by more than 19%

(D)

Increases by more than 19%

Question-7

The escape velocity for a body projected vertically upwards from the surface of earth is 11km/s. If the body is projected at an angle of 45° with the vertical, the escape velocity will be :

(A)

11km/s

(B)

11/√2 m/s

(C)

11√2 km/s

(D)

22 km/s

Question-8

The time period of an earth satellite in circular orbit is independent of :

(A)

both the mass and radius of the orbit

(B)

neither the mass of the satellite nor the radius of its orbit

(C)

the mass of the satellite

(D)

radius of its orbit

Question-9

An infinity number of point masses each equal to m are placed at x = 1, x = 2, x = 4, x = 8, ..... What is the total gravitational potential at x - 0?

(A)

-Gm

(B)

-2Gm

(C)

-4Gm

(D)

-8 Gm

Question-10

g_{e} and g_{p} are accelerations due to gravity on the surface of earth and a planet respectively. The radius and mass of the planet are double the radius and mass of earth. Then :

(A)

g_{e} = g_{p}

(B)

g_{e} = 2g_{p}

(C)

g_{p} = 2g_{e}

(D)

g_{e} = √2g_{p}

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