Question

The pulley shown in figure has radius $20$ cm and moment of inertia $0.2$ kg $m^2$. Spring used has force constant $50$ N$m^{-1}$. The system is released from the rest. Find the velocity of $1$ kg block when it has descended $10$ cm.

• A. $\frac{1}{2}m{s}^{-1}$
• B. $\frac{1}{\sqrt{2}}m{s}^{-1}$
• C. $\frac{1}{\sqrt{3}}m{s}^{-1}$
• D. none

Answer 1

The correct option is A $\frac{1}{2}m{s}^{-1}$

$mgx=\frac{1}{2}k{x}^2+\frac{1}{2}I{\omega }^2+\frac{1}{2}m{v}^2$
$1\left(10\right)\left(.1\right)=\frac{1}{2}\left[50\right(.1{)}^2+\left(.2\right){\left(\frac{v}{.2}\right)}^2+1\left(v^2\right)]$
$\Rightarrow 2=0.5+6v^2$
or
$v=\frac{1}{2}m{s}^{-1}$