First slide

Rotational motion

Question

A block of mass m is attached to a pulley disc of equal mass m and radius r by means of a slack string as shown. The pulley is hinged about its centre on a horizontal table and the block is projected with an initial velocity of 5 m/s. Its velocity when the string becomes taut will be

Moderate

A

3 m/s
B

2.5 m/s
C

5/3 m/s
D

10/3 m/s

Solution

When the string becomes taut, according to string constraint, the velocity of block will be same as tangential velocity of other end of string connected with disc.
Apply conservation of angular momentum about the hinge,
we get,
$\begin{array}{l} m v R = \frac{m}{2} R^{2} ω + m v' R \\ \Rightarrow m v R = \frac{m}{2} R^{2} ω + m (R ω) R \\ \Rightarrow R ω = \frac{2 v}{3} = \frac{2 \times 5}{3} = \frac{10}{3} m / s \\ \Rightarrow v' = R ω = \frac{10}{3} m / s \end{array}$

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