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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 atr=r0 be V0, then what is the expression for the gravitational potential (V).

A
k log (rr0)
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B
k log (r0r)
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C
V0+klog(rr0)
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D
V0+klog(r0r)
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Solution

## The correct option is B V0+klog(rr0)Gravitational potential V=−∫→E.→drVr−Vo=−∫rro→E.→drVr−Vo=−∫rro−|E|drVr−Vo=∫rro|E|drVr−Vo=∫rrokrdrVr−Vo=klog(r)∣∣∣rroVr−Vo=klog(r)−klog(ro) (using loga−logb=log[ab])Vr=Vo+klog(rro)

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