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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.dr
VrVo=rroE.dr
VrVo=rro|E|dr
VrVo=rro|E|dr
VrVo=rrokrdr
VrVo=klog(r)rro
VrVo=klog(r)klog(ro) (using logalogb=log[ab])
Vr=Vo+klog(rro)

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