Q 11-06-044JEE MainJEE Main 2026 (6 Apr, Shift 1)Medium
A solid sphere of radius $4$ cm and mass $5$ kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of $1200$ rpm. It is brought to rest in $10$ s by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are ______ and ______ respectively.
Answer: (D) $0.0128\pi$ Nm, $100$
$I = \dfrac{2}{5}MR^2 = \dfrac{2}{5} \times 5 \times (0.04)^2 = 3.2 \times 10^{-3}$ kg m².
$\omega_0 = 1200 \times \dfrac{2\pi}{60} = 40\pi$ rad/s, so $\alpha = \dfrac{40\pi}{10} = 4\pi$ rad/s².
$\tau = I\alpha = 3.2 \times 10^{-3} \times 4\pi = 0.0128\pi$ N m.
Angle turned: $\theta = \dfrac{\omega_0 t}{2} = 200\pi$ rad $= 100$ rotations.
Solution by Sreeraj P, M.Sc Physics