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

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Important Questions on Gravitation

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Achieve Indian Airforce Agniveer Vayu Physics Practice Book>Chapter 8 - Gravitation>Exercise>Q 7

An astronaut of mass

m

is working on a satellite orbiting the earth at a distance

h

from the earth's surface. The radius of the earth is

R

, while its mass is

M

. The gravitational pull

F_{G}

on the astronaut is

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Achieve Indian Airforce Agniveer Vayu Physics Practice Book>Chapter 8 - Gravitation>Exercise>Q 8

Different points in the earth are at slightly different distances from the sun and hence, experience different forces due to gravitation. For a rigid body, we know that if various forces act at various points in it, the resultant motion is as if a net force acts on the

C M

(centre of mass) causing translation and a net torque at the

C M

causing rotation around an axis through the

C M

. For the earth sun system (approximating the earth as a uniform density sphere),

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Achieve Indian Airforce Agniveer Vayu Physics Practice Book>Chapter 8 - Gravitation>Exercise>Q 9

The mass of the moon is

(1 / 8)

mass of the earth but the gravitational pull is

(1 / 6)

the pull of the earth. It is due to the fact that

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Achieve Indian Airforce Agniveer Vayu Physics Practice Book>Chapter 8 - Gravitation>Exercise>Q 1

g

is the acceleration due to gravity on the surface of earth, it's value at a height equal to double the radius of earth is:

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Agniveer Vayu

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Achieve Indian Airforce Agniveer Vayu Physics Practice Book>Chapter 8 - Gravitation>Exercise>Q 2

If the value of g acceleration due to gravity at earth surface is

10 m s^{- 2}

. Its value in

m s^{- 2}

at the centre of the earth, which is assumed to be a sphere of radius

R

metre and uniform mass density is

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Agniveer Vayu

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Achieve Indian Airforce Agniveer Vayu Physics Practice Book>Chapter 8 - Gravitation>Exercise>Q 3

Two planets of radii in the ratio

2 : 3

are made from the material of density in the ratio

3 : 2

. Then, the ratio of acceleration due to gravity

\frac{g_{1}}{g_{2}}

at the surface of the two planets will be

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Agniveer Vayu

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Achieve Indian Airforce Agniveer Vayu Physics Practice Book>Chapter 8 - Gravitation>Exercise>Q 4

At what height from the surface of earth the gravitation potential and the value of g are

- 5.4 \times 10^{7} J k g^{- 2}

and

6.0 m s^{- 2}

respectively? Take the radius of earth as

6400 km

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Agniveer Vayu

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Achieve Indian Airforce Agniveer Vayu Physics Practice Book>Chapter 8 - Gravitation>Exercise>Q 5

A body weighs

w

Newton at the surface of the earth. Its weight at a height equals to half the radius of the earth, will be

Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to -

Important Questions on Gravitation

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