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Question

If g represents the gravitational field due to a solid sphere of radius R, then a plot of $g R^{3}$ v/s R in the region from r=0 to r=R will be

A

A straight line parallel to Y-axis

B

A straight line parallel to X-axis

C

A straight line passing through the origin, whose slope is GM

D

A straight line passing through the origin, whose slope is g

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Solution

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Correct option is C)

We know that field inside a solid sphere is given by $g = G M x / R^{3} ⟹ g R^{3} = G M x$

Thus a plot of $g R^{3}$ v/s x will give rise to a straight line , whose slope is GM

The correct option is (c)

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