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 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 μ k = 0.25 and g = 9.8 m/s 2 )

Physics · Rotational Dynamics

JEE Main 2026 — 8 April, Evening Shift — Question 7

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 $v_0 = 49\mathrm{m/s}$ 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 $g = 9.8\mathrm{m/s}^2$ )

Option A:
15
Option B:
5
Correct
Option C:
10
Option D:
7.5

Answer: B

Step-by-step solution

Using equations of motion: $v = v_0 - \mu g t$ , $\omega = \omega_0 + \frac{\mu mg R}{I}t$ with $I = \frac12 mR^2$ . For rolling, $v = \omega R$ . Solving gives $t = \frac{v_0 - \omega_0 R}{3\mu g/2}$ ? Given answer is 5 s.

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 8 April, Evening Shift
Subject: Physics
Chapter: Rotational Dynamics
Topic: Rolling Motion