Q 11-13-041JEE MainJEE Main 2026 (4 Apr, Shift 2)Medium
A uniform disc of radius $R$ and mass $M$ is free to oscillate about the axis $A$ as shown in the figure. For small oscillations the time period is ______.
($g$ is acceleration due to gravity)
Answer: (A) $2\pi\sqrt{\dfrac{5R}{4g}}$
The axis $A$ is a tangent to the disc lying in its plane. By the perpendicular and parallel axis theorems:
$$I = \frac{MR^2}{4} + MR^2 = \frac{5}{4}MR^2$$
For a physical pendulum with the centre of mass at distance $R$ from the axis:
$$T = 2\pi\sqrt{\frac{I}{MgR}} = 2\pi\sqrt{\frac{5R}{4g}}$$
Solution by Sreeraj P, M.Sc Physics