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Question

In a certain region of space, the gravitational field is given by kr, where r is the distance and k is a constant. If the gravitational potential at r=r0 be V0, then what is the expression for the gravitational potential V?

A
k lnrr0
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B
k lnr0r
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C
V0+k lnrr0
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D
V0+k lnr0r
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Solution

The correct option is C V0+k lnrr0
Given that,
Gravitational field, E=kr
The relation between gravitational (E) field and gravitational potential is given by
dV=E.dr
The change in potential is given by,
VV0dV=rr0krdr
VV0=k{ ln r}rr0
V=V0+k ln rr0

Hence, option (c) is correct.

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