State the laws of Gravitation. Obtain an expression for the gravitational potential due to mass M at a distance R . Show that T 2 R 3 is constant for a satellite orbiting the earth where T and R have usual meaning.

Newton's law of gravitation states that any matter in the universe will apply a force on the other body.This force is attractive in nature.It is directly proportional to product of masses of the two bodies and inversely proportional to square of distance between them. Let there be a small mass m at distance r from the mass M of which we have find the gravitational potential. There will be force of attraction ,given by F g = G M m r 2 . Work done in moving the body against this force by distance d r is given by : d W = F g × d r = G M m r 2 d r ⇒ W = ∫ d W = ∫ ∞ R G M m r 2 d r = - G M m 1 r ∞ R = - G M m R T ( t i m e p e r i o d ) of a satellite is given by T = 2 π R 3 GM 1 2 Therefore , T 2 = 4 π 2 R 3 GM ⇒ T 2 R 3 = 4 π 2 GM = c o n s tan t

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Bureau's Higher Secondary Physics Class 11>Chapter 7 - Gravitation>MODEL QUESTIONS>Q 13

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11th Odisha Board

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The Mount Everest is $8848 m$ above sea level, Find the acceleration due to gravity at Mount Everest given the value of $g$ at the surface of earth is $9.8 m S^{- 2}$ and mean radius of the earth is $6.37 \times 10^{6} m$ . Neglect earth's rotation about its axis.

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Important Questions on Gravitation

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11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Physics Class 11>Chapter 7 - Gravitation>MODEL QUESTIONS>Q 14

How much energy in $10^{9} Joules$ must be given to a $100 kg$ rocket missile to carry it from the surface of earth into free space? Given mass of earth $= 6 \times 10^{24} kg$