A solid cylinder having radius R and length L is slipping on a rough… | JEE Main 2026 (8 Apr, Shift 2)

Q9JEE Main 2026 · 8 APR · SHIFT 2Difficult

Rolling Motion

A solid cylinder having radius $R$ and length $L$ is slipping on a rough horizontal plane. At time $t = 0$ the cylinder has a translational velocity $v_0 = 49\text{ m/s}$ , perpendicular to its axis and a rotational velocity $v_0/4R$ about the centre. The time taken by the cylinder to start rolling is ______ seconds. (coefficient of kinetic friction $\mu_K = 0.25$ and $g = 9.8\text{ m/s}^{2}$ )

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Answer: (b)

Since $v_0 > \omega_0 R$ , friction $\mu mg$ acts backward: $v = v_0 - \mu g t$ .
Torque $\mu mgR = \frac{1}{2}mR^2\alpha \Rightarrow \alpha = \dfrac{2\mu g}{R}$ , so $\omega R = \dfrac{v_0}{4} + 2\mu g t$ .
Rolling when $v = \omega R$ : $v_0 - \mu g t = \dfrac{v_0}{4} + 2\mu g t \Rightarrow t = \dfrac{v_0}{4\mu g}$ .
$t = \dfrac{49}{4 \times 0.25 \times 9.8} = 5$ s, so the answer is (b).

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Rolling Motion question from JEE Main 2026 (8 Apr, Shift 2)

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