Assertion: A rigid disc rolls without slippin | vedclass

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Question

(D) For a disc rolling without slipping on a horizontal rough surface with uniform angular velocity $\omega$,the velocity of the point of contact is z

Vedclass · Accepted Answer

If the $Assertion$ is incorrect but $Reason$ is correct.

Vedclass · Answer

(D) For a disc rolling without slipping on a horizontal rough surface with uniform angular velocity $\omega$,the velocity of the point of contact is zero.However,the acceleration of the lowest point is not zero.The acceleration of any point on the rim of the disc consists of two components: centripetal acceleration $(a_c = \omega^2 R)$ directed towards the center and tangential acceleration $(a_t = \alpha R)$.Since the angular velocity is uniform,$\alpha = 0$,so $a_t = 0$.The centripetal acceleration $a_c = \omega^2 R$ is directed vertically upwards towards the center of the disc.Therefore,the net acceleration of the lowest point is $\omega^2 R$ (upwards),which is non-zero.Thus,the $Assertion$ is incorrect and the $Reason$ is correct.

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