Solve

Guides

0

You visited us 0 times! Enjoying our articles? Unlock Full Access!

Question

Two identical spherical masses are kept at some distance as shown. Potential energy when a mass m is taken from the surface of one sphere to the other

decreases continuously
increases continuously
first increases, then decreases
first decreases, then increases

A

first increases, then decreases

B

decreases continuously

C

first decreases, then increases

D

increases continuously

Open in App

Solution

Verified by Toppr

Gravitational potential energy between two masses $(M)$ separated by a distance $R$ is $- G M M / R = - G M^{2} / R$ .
When a small mass m is taken out of mass M, and kept at a distance x from (M-m), the total PE of the system becomes $- G M m / (R - x) - G m (M - m) / x - G M (M - m) / R$
As m moves towards M, the gravitational PE in the system will increase. Mass (M-m) will attract mass m and external for will be required to move m away from (M-m).
Once mass m reaches a point P where $R_{1}$ is the distance between mass m and M and $R_{2}$ is the distance between m and (M-m) and $R_{1}$ and $R_{2}$ related as $R_{1} / R_{2} = \sqrt{M / (M - m)}$ , the potential energy on mass m will be zero. At this point mass m will not experience any force.
As mass m stars moving towards mass M, the PE will decrease as mass M will attract mass m.
So, in this situation, PE of the total system will increase first and then decrease.

Was this answer helpful?

3

Similar Questions

Q1

Two identical spherical masses are kept at some distance as shown. Potential energy when a mass m is taken from the surface of one sphere to the other

View Solution

Q2

Two identical spherical masses of mass

M

are kept at some distance. Potential energy of the system when a mass

M

is taken from the surface of one of the sphere to the other

View Solution

Q3

Two identical positive charges are fixed on x-axis at +a and -a. A charge particle of mass m is released from rest under gravity from some height along y-axis. The particle just reaches origin, then choose correct options.

View Solution

Q4

Assertion :There are two identical spherical bodies fixed in two positions as shown. While moving from

A

to

B

gravitational potential first increases then decreases. Reason: At centre of

A

and

B

field strength will be zero.

View Solution

Q5

Two equal positive charges are kept at points A and B. The electric potential at the points between A and B (excluding these points) is situated while moving from A to B. The potential
(a) continuously increases
(b) continuously decreases
(c) increases then decreases
(d) decreases then increases

View Solution