JEE Main 2025 Apr 2 Shift 2, Physics Q21: Law of Rotation And Work-Energy Theorem

JEE Main2025Apr 2, Shift 2Physics

Q.

A wheel of radius $0.2$ m rotates freely about its center when a string that is wrapped over its rim is pulled by force of $10$ N as shown in figure. The established torque produces an angular acceleration of $2$ rad/s $^{2}$ . Moment of inertia of the wheel is ________ kg m $^{2}$ .

(Acceleration due to gravity $= 10$ m/s $^{2}$ )

Your answer

Solution

The string pulls tangent to the rim, producing a torque about the central axis:

$τ = F \cdot R = 10 \times 0.2 = 2 N\cdotm$ .

Using $τ = I α$ :

$I = \frac{τ}{α} = \frac{2}{2} = 1 kg\cdotm^{2}$ .

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