A satellite is launched into a circular orbit of radius ‘R’ around earth while a second satellite is launched into an orbit of radius 1.02 R. The percentage difference in the time periods of the two satellites is

(a) 0.7                                (b) 1.0

(c) 1.5                                 (d) 3

Concept Questions :-

Kepler laws
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Difficulty Level:

If the radius of the earth shrinks by 1.5% (mass remaining same), then the value of acceleration due to gravity changes -

(a)  1%         (b)   2%

(c)  3%         (d)   4%

Concept Questions :-

Acceleration due to gravity
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Difficulty Level:

Distance of geostationary satellite from the surface of the earth  in terms of ${R}_{e}$ is

(a)                          (b)

(c)                             (d)

Concept Questions :-

Satellite

Difficulty Level:

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

(a)    $GMm/12{R}^{2}$                (b)    $GMm/3{R}^{2}$

(c)     $GMm/8R$                  (d)     $GMm/6R$

Concept Questions :-

Gravitational potential energy
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Difficulty Level:

If radius of the earth contracts by 2% and its mass remains the same, then weight of the body at the earth surface :

(a)     Will decrease                       (b)  Will increase

(c)   Will remain the same              (d)  None of these

Concept Questions :-

Acceleration due to gravity
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Difficulty Level:

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

(a)   mgR/2                 (b)  2 mgR

(c)   mgR                    (d)   mgR/4

Concept Questions :-

Escape velocity
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Difficulty Level:

A satellite is to revolve round the earth in a circle of radius 8000 km. The speed at which this satellite be projected into an orbit, will be
(a)                       (b) 16 km/s

(c) 7.15 km/s                   (d) 8 km/s

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Difficulty Level:

If mass of a body is M on the earth surface, then the mass of the same body on the moon surface is

(a)  M/6       (b)  Zero

(c)  M          (d)   None of these

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Difficulty Level:

Radius of orbit of satellite of earth is R. Its kinetic energy is proportional to -

(a) $\frac{1}{R}$                       (b) $\frac{1}{\sqrt{R}}$

(c) R                         (d)  $\frac{1}{{R}^{3/2}}$

Concept Questions :-

Gravitational potential energy
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Difficulty Level:

A particle falls towards earth from infinity. It’s velocity on reaching the earth would be -

(a)   Infinity                   (b) $\sqrt{2gR}$

(c)   $2\sqrt{gR}$                    (d)  Zero

Concept Questions :-

Escape velocity