Question

A horizontal plane supports a stationary vertical cylinder of radius R and a disc attached to the cylinder by a horizontal thread AB of length l₀ as shown in the fig. Disc is given a velocity v₀. How long will it takes to strike the cylinder. Assume no friction.

• A. $\frac{l_{0}}{v_{0}}$
• B. $\frac{l_{0}^{2}}{Rv_{0}}$
• C. $\frac{l_{0}^{2}}{2Rv_{0}}$
• D. $\frac{l_{0}^{2}}{3Rv_{0}}$

Answer 1

Answer: (C)

$\frac{l_{0}^{2}}{2Rv_{0}}$

Answer 2

Let s be the total distance covered by disc.

Then t = $\frac{s}{v_{0}}$.

At any instant ds = (l₀ - Rθ)dθ

∴ s = $\int_{0}^{l_{0}/R}{\left( l_{0} - R\theta \right)d\theta = \frac{l_{0}^{2}}{R} - \frac{l_{0}^{2}}{2R}} = \frac{l_{0}^{2}}{2R}$

∴ t = $\frac{l_{0}^{2}}{2Rv_{0}}$