Exam

AIIMS

Year

2019

Date

25 May

Subject

Physics

Chapter

Rotational Motion

AIIMS 2019 · 25 May · Physics · Rotational Motion

A disc of radius 20 ~cm and mass 1 / 2 ~kg is rolling on an...

A disc of radius $20 \mathrm{~cm}$ and mass $1 / 2 \mathrm{~kg}$ is rolling on an inclined plane. Find out the frictional force such that disc performs pure rolling.

Step-by-step solution

Let $m$ be the mass and $R$ be the radius of the disc. $m g \sin \theta-f=m a_{c m}$$\begin{aligned} & \tau_{c m}=I_{c m^\alpha} \\ & f R=\frac{m R^2}{2}\left(\frac{a_{c m}}{R}\right)\end{aligned}$$f=\frac{m a_{c m}}{2} or a_{c m}=\frac{2 f}{m}$ So, $m g \sin \theta-f=m\left(\frac{2 f}{m}\right) f=\frac{m g \sin \theta}{3}=\frac{1}{2} \times \frac{10}{3} \times \frac{1}{\sqrt{2}}=\frac{5}{3 \sqrt{2}} \mathrm{~N}$