A disc of mass m and radius r is free to rotate about its centre as shown in the figure. A string is wrapped over its rim and a block of mass m is attached to the free end of the string. The system is released from rest. The speed of the block as it descends through a height h, is

Question

A disc of mass m and radius r is free to rotate about its centre as shown in the figure. A string is wrapped over its rim and a block of mass m is attached to the free end of the string. The system is released from rest. The speed of the block as it descends through a height h, is (A) √2 g h (B) √(2/3) g h (C) 2 √(g h/3) (D) (1/2) √3 g h

Tardigrade Admin · Accepted Answer

Using Mechanical energy conservation m g h=(1/2) m v2+(1/2)((1/2)) m r2 ⋅ (v2/r2) m g h=(3/4) m v2 v2=(4 g h/3) v=√(4 g h/3)

Q. A disc of mass $m$ and radius $r$ is free to rotate about its centre as shown in the figure. A string is wrapped over its rim and a block of mass $m$ is attached to the free end of the string. The system is released from rest. The speed of the block as it descends through a height $h$ , is

$2 g h$

$\frac{2}{3} g h$

$2 \frac{g h}{3}$

$\frac{1}{2} 3 g h$

Using Mechanical energy conservation
$m g h = \frac{1}{2} m v^{2} + \frac{1}{2} (\frac{1}{2}) m r^{2} \cdot \frac{v ^{2}}{r ^{2}}$
$m g h = \frac{3}{4} m v^{2}$
$v^{2} = \frac{4 g h}{3}$
$v = \frac{4 g h}{3}$

Q. A disc of mass m and radius r is free to rotate about its centre as shown in the figure. A string is wrapped over its rim and a block of mass m is attached to the free end of the string. The system is released from rest. The speed of the block as it descends through a height h, is

2gh​

32​gh​

23gh​​

21​3gh​