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Question

The gravitational field due to a mass distribution is given by E=K/x3 in xdirection. Taking the gravitational potential to be zero at infinity, find its value at a distance x.

A
K2x2
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B
K3x2
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C
2K3x2
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D
3K2x2
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Solution

The correct option is A K2x2
The change in potential in going from the initial to find position in a gravitational field E is given by

fidV=fiEdr

Since the change in field is only in the x direction

xdV=xEdx=xKx3dx

VxV=Kx1x3dx=K[12x2]x

As we know that V=0

Vx=K2[1x212]=K2x2

Hence, option (a) is correct.

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