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A small planet is revolving around a very massive star in a circular orbit of radius $R$ with a period of revolution $T$ . If the gravitational force between the planet and the star is proportional to $R^{- \frac{5}{2}}$ , then $T$ would be proportional to,

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Important Questions on Gravitation

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Gamma Question Bank for Engineering Physics>Chapter 7 - Gravitation>Assignment>Q 46

E, U

and

K

represent total mechanical energy, potential energy and kinetic energy of a satellite revolving around a planet. Which of the following quantity is not independent of orbital radius of the satellite?

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Gamma Question Bank for Engineering Physics>Chapter 7 - Gravitation>Assignment>Q 47

v_{0}

be the orbital velocity of an artificial satellite orbiting just above the earth's surface, then the orbital velocity of the same satellite orbiting at an altitude equal to earth's radius is

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Gamma Question Bank for Engineering Physics>Chapter 7 - Gravitation>Assignment>Q 48

The period of revolution of a satellite orbiting Earth at a height

4 R

above the surface of Earth is

x hrs

, where

R

is the radius of earth. The period of another satellite at a height

1.5 R

from the surface of the Earth is

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Gamma Question Bank for Engineering Physics>Chapter 7 - Gravitation>Assignment>Q 49

A particle is projected vertically upward with velocity

\sqrt{\frac{2}{3} \frac{G M}{R}}

from the surface of Earth. The height attained by it is (

G, M, R

have usual meanings)

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Gamma Question Bank for Engineering Physics>Chapter 7 - Gravitation>Assignment>Q 50

Identify the incorrect statement about a planet revolving around Sun.

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Gamma Question Bank for Engineering Physics>Chapter 7 - Gravitation>Assignment>Q 51

Suppose a tunnel is made in earth which passes, through its centre. If an object is dropped from height

\frac{R}{2}

from earth surface above the tunnel. If its speed at depth

\frac{R}{2}

from earth surface in tunnel is

\sqrt{\frac{N G M}{12 R}}

, then value of

N

is (Given

M

is mass of earth and

R

is radius of earth).

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Gamma Question Bank for Engineering Physics>Chapter 7 - Gravitation>Assignment>Q 52

Six stars of equal masses

M

are moving about the centre of mass of the system such that they are always on the vertices of a regular hexagon of side length a. If their time period of motion is

2 π \sqrt{\frac{N \sqrt{3} a^{3}}{G M (5 \sqrt{3} + N)}}

then value of

N

is ____.

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Gamma Question Bank for Engineering Physics>Chapter 7 - Gravitation>Assignment>Q 53

A planet is revolving around the sun in an elliptical orbit. If the speed of planet at shown position $P$ ( $M$ :Mass of Sun) is $\sqrt{\frac{k G M}{2 a}}$ , then value of $k$ is ______.

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A small planet is revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force between the planet and the star is proportional to R-52, then T would be proportional to,

Important Questions on Gravitation

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A small planet is revolving around a very massive star in a circular orbit of radius $R$ with a period of revolution $T$ . If the gravitational force between the planet and the star is proportional to $R^{- \frac{5}{2}}$ , then $T$ would be proportional to,