Statement-1: KE of rotating rigid body in CM frame is $\frac{1}{2} I_{c m} ω^{2}$ where symbols have usual meaning.
Statement-2: In CM frame rigid body can have only pure rotational motion.

Statement-1 is true,statement-2 is true and statement-2 is correct explanation for statement-1.

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Statement-1 is true,statement-2 is true and statement-2 is NOT the correct explanation for statement-1.

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Statement-1 is true,statement-2 is false.

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Statement-1 is false, statement-2 is true.

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Solution

The correct option is D Statement-1 is true,statement-2 is true and statement-2 is correct explanation for statement-1.
The sphere is stationary at one point when CM frame of reference is selected. Only the rotation of the rigid body is the relevant motion. Thus the KE in this case is $\frac{1}{2} I_{c m} ω^{2}$

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Statement-1: KE of rotating rigid body in CM frame is 12Icmω2 where symbols have usual meaning. Statement-2: In CM frame rigid body can have only pure rotational motion.

The correct option is D Statement-1 is true,statement-2 is true and statement-2 is correct explanation for statement-1.The sphere is stationary at one point when CM frame of reference is selected. Only the rotation of the rigid body is the relevant motion. Thus the KE in this case is 12Icmω2

Statement-1: KE of rotating rigid body in CM frame is $\frac{1}{2} I_{c m} ω^{2}$ where symbols have usual meaning.
Statement-2: In CM frame rigid body can have only pure rotational motion.