Assertion :Centre of mass of a rigid body always lies inside the body. Reason: Centre of mass and centre of gravity coincide if gravity is uniform.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is D Assertion is incorrect but Reason is correct
Assertion:
CM of a ring with a hole at the centre is at the centre of the ring which is not a point in the material of the ring( see figure).
Hence, assertion is wrong.
Reason:
Consider a two particle system. If there is variation in g from the location of mass $m_{1}$ to mass $m_{2}$ as denoted by $g_{1}$ and $g_{2}$ , g will not cancel out from numerator and denominator as shown in the expression for $X_{C G}$ below. If g does not vary, $X_{C M}$ will coincide with $X_{C G}$
$X_{C M} = \frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}}$ ;
$X_{C G} = \frac{m_{1} g_{1} x_{1} + m_{2} g_{2} x_{2}}{m_{1} g_{1} + m_{2} g_{2}}$ ;
Hence, reason is correct.
Answer:
Option (D)

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