JEE Mains · Physics · STD 11 - 6. system of particles and rotational 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 \(v_0=49\) 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 \(g=9.8\) m/s\(^2\))
- A \(15\)
- B \(5\)
- C \(10\)
- D \(7.5\)
Answer & Solution
Correct Answer
(B) \(5\)
Step-by-step Solution
Detailed explanation
Initial translational velocity, \(v_0 = 49\) m/s. Initial angular velocity, \(\omega_0 = \dfrac{v_0}{4R}\). Velocity of the lowest point of the cylinder is \(v_{bottom} = v_0 - \omega_0 R = v_0 - \dfrac{v_0}{4} = \dfrac{3v_0}{4} > 0\). Since the lowest point is slipping forward,…
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