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Question

# In a certain region of space, the gravitational field is given by âˆ’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 lnrr0Given 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, ⇒V∫V0dV=−r∫r0−krdr ⇒V−V0=k{ ln r}rr0 ⇒V=V0+k ln rr0 Hence, option (c) is correct.

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