Question

An empty bucket of mass $1kg$ attached by a light cord passed over a pulley of a water well is released from rest. If the pulley assembly is assumed to be a uniform solid cylinder of mass $8kg$ and free to rotate about its axis without any friction, then the speed of the bucket as it hits the water $16m$ below is
(take, $g=10m{s}^{-2}$ )

• A. $4m{s}^{-1}$
• B. $8m{s}^{-1}$
• C. $16m{s}^{-1}$
• D. $20m{s}^{-1}$

Answer 1

Answer: (B)

Torque on pulley $=I\alpha$
$\Rightarrow mgR=\frac{M{R}^2\alpha }{2}$
$\alpha =\frac{2mg}{MR}$
So, acceleration of rope, $a=R\alpha$
$=R\cdot \frac{2mg}{MR}=\frac{2mg}{M}$
$=\frac{2\times 1\times 10}{8}=\frac{10}{4}m{s}^{-2}$
Speed of bucket as it falls by $16m$ is
$v=\sqrt{2\times a\times s}=\sqrt{2\times \frac{10}{4}\times 16}$
$=\sqrt{80}=8.6\approx 8m{s}^{-1}$