Physics - Rotation Question with Solution | TestHub

Question Explanation: We need to identify the correct statements about the motion of a disc rolling on a horizontal surface while revolving around a pivot, given that the speed of its centre of mass is constant and equal to v. Concept: Circular motion of centre of mass and rolling constraint. Solution: The center of mass of the disc moves in a circular path of radius R about the pivot with constant speed v . Hence, the center of mass executes uniform circular motion. For uniform circular motion: Centripetal acceleration of center of mass, ${\mathrm{a}}_{\mathrm{c}}={\mathrm{v}}^2/\mathrm{R}\Rightarrow$ Statement (3) is correct. Since the speed of the center of mass is constant, there is no change in the magnitude of velocity. Therefore, tangential acceleration of the center of mass is zero. ⇒ Statement (4) is correct. The disc is rolling while revolving, so its angular velocity is not necessarily constant. Hence, angular acceleration of the disc need not be zero. ⇒ Statement (1) is incorrect. The center of mass is moving in a circular path, so its centripetal acceleration cannot be zero. ⇒ Statement (2) is incorrect. Final Answer: Option (3) and (4)