Question

A solid disc of mass 16-kg and radius 50 cm has a mass of 4-kg hanging from one side by a massless string. The disc acts like a frictionless pulley and rotates freely about its center. Once released from rest, how much time does it take for the wheel to rotate through 20 revolutions? (A) 2 Squareroot 2 pi seconds (B) Squareroot 2 pi seconds (c) 2 Squareroot pi seconds) D) Squareroot pi/2 seconds

Answer 1

By using Free Body Diagram we can write equilibrium equations

For Block of 4Kg

Where T is tension in the string and a is acceleration downwards.

Similarly, For disc,

As there is no slipping $a = r\alpha$

So, Equation for disc will be

$Tr = \frac{1}{2}16r^2*\frac{a}{r}$ $Tr = I\alpha$

Use this valye of T in equation og block

$a = \frac{g}{3}$

Diatnce travelled by block = $20*2\pi*0.5 = 20\pi$

By equation of motion

$S = ut + \frac{1}{2}at^2$

$20\pi = \frac{1}{2}*\frac{10}{3}t^2$

$t = 2 \sqrt{3\pi} sec$

This is not given in the option.