The gravitational potential energy of a two-particle system is derived in this chapter as U = - G m 1 m 2 r . Does it follow from this equation that the potential energy for r = ∞ must be zero? Can we choose the potential energy for r = ∞ to be 20 J and still use this formula? If no, what formula should be used to calculate the gravitational potential energy at separation r ?

In the given formula U = - G m 1 m 2 r , r is the separation between the particles, not the position of the particles. If the separation is too large then, the gravitational potential energy between them is almost zero. The zero of potential is taken to be infinity by choice, by assuming that there is no gravitational field very far away from the reference mass. Hence, if we say ∆ U = U ( r ) - U ( ∞ ) and if we assume U ( ∞ ) = 0 , we obtain, ∆ U = U ( r ) = - G m 1 m 2 r . Hence, the potential energy at infinity being zero is not followed from this equation, but rather it is, its cause. If it is assumed that the particle has an energy of 20 J at infinity, then, as per the equation, ∆ U ' = U ' r = U ( r ) + C Putting, r → ∞ ∆ U ' = 20 J ⇒ U ' r = 20 J ⇒ U r + C = 20 J ⇒ - G M m r + C = 20 J ⇒ C = 20 J r → ∞ ⇒ - G M m r = 0 ⇒ U ' r = - G M m r + 20 J .

HARD

JEE Main

IMPORTANT

Earn 100

Suppose the gravitational potential due to a small system is $\frac{k}{r^{2}}$ at a distance $r$ from it. What will be the gravitational field? Can you think of any such system? What happens if there were negative masses?

Important Questions on Gravitation

MEDIUM

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 11 - Gravitation>QUESTIONS FOR SHORT ANSWERS>Q 9

The gravitational potential energy of a two-particle system is derived in this chapter as $U = - G \frac{m_{1} m_{2}}{r}$ .

Does it follow from this equation that the potential energy for $r = \infty$ must be zero?

Can we choose the potential energy for $r = \infty$ to be $20 J$ and still use this formula? If no, what formula should be used to calculate the gravitational potential energy at separation $r$ ?

MEDIUM

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 11 - Gravitation>QUESTIONS FOR SHORT ANSWERS>Q 10

The weight of an object is more at the poles than at the equator. Is it beneficial to purchase goods at equator and sell them at the pole? Does it matter whether a spring balance is used or an equal-beam balance is used?

MEDIUM

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 11 - Gravitation>QUESTIONS FOR SHORT ANSWERS>Q 11

The weight of a body at the poles is greater than the weight at the equator. Is it the actual weight or the apparent weight we are talking about? Does your answer depend on whether only the earth's rotation is taken into account or the flattening of the earth at the poles is also taken into account?

EASY

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 11 - Gravitation>QUESTIONS FOR SHORT ANSWERS>Q 12

If the radius of the earth decreases by

1 %

without changing its mass, will the acceleration due to gravity at the surface of the earth increase or decrease? If so, by what percent?

MEDIUM

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 11 - Gravitation>QUESTIONS FOR SHORT ANSWERS>Q 13

A nut becomes loose and gets detach from a satellite revolving around the earth. Will it land on the earth? If yes, where will it land? If no, how can an astronaut make it land on the earth?

MEDIUM

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 11 - Gravitation>QUESTIONS FOR SHORT ANSWERS>Q 14

Is it necessary for the plane of the orbit of a satellite to pass through the centre of the earth?

MEDIUM

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 11 - Gravitation>QUESTIONS FOR SHORT ANSWERS>Q 15

Consider earth satellites in circular orbits. A geostationary satellite must be at a height of about

36000 km

from the earth's surface. Will any satellite moving at this height be a geostationary satellite? Will any satellite moving at this height have a time period of

24

hours?

MEDIUM

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 11 - Gravitation>QUESTIONS FOR SHORT ANSWERS>Q 16

No part of India is situated on the equator. Is it possible to have a geostationary satellite which always remains over New Delhi?

Suppose the gravitational potential due to a small system is kr2 at a distance r from it. What will be the gravitational field? Can you think of any such system? What happens if there were negative masses?

Important Questions on Gravitation

Learn and Prepare for any exam you want !

Suppose the gravitational potential due to a small system is $\frac{k}{r^{2}}$ at a distance $r$ from it. What will be the gravitational field? Can you think of any such system? What happens if there were negative masses?