JEE Main 2026 · 6 Apr · Shift 1 · Physics Q31

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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.

0.128\pi

Nm, 100

0.0128\pi

Nm, 50

0.128\pi

Nm, 50

0.0128\pi

Nm, 100

Answer and worked solution

Official answer: D

Moment of inertia. $I=\tfrac25(5)(0.04)^2=0.0032$ kg m².

Deceleration. $\omega_0=1200$ rpm $=40\pi$ rad/s, stopped in 10 s, so $\alpha=4\pi$ rad/s².

Torque. $\tau=I\alpha=0.0128\pi$ N m.

Rotations. Average speed 10 rev/s for 10 s: 100 rotations.

(D)

Topics:Torque and rotational dynamics Moment of inertia

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JEE Main 2026 · 6 Apr · Shift 1, Physics question 31