Question

A tangential force $F$ acts at the top of a disc of mass $m$ and radius $R$. If it rolls without slipping. Then

• A. Acceleration of disc $= \frac {2F}{3m}$
• B. Friction force between disc and surface$= \frac {2F}{3}$
• C. Acceleration of disc$= \frac {6F}{5m}$
• D. Friction force between disc and surface is $= \frac{F}{3}$

Answer 1

Answer: (D)

Equation regarding translatory motion
$F + f = ma \quad ...(i)$
Equation regarding rotational motion
$FR - fR = \frac{mR^2}{2} \frac{a}{R} \quad ...(ii)$
From equation $(i)$ and $(ii)$
$2F= \frac{3ma}{2}$ or $a = \frac{4F}{3m} $
Also, $F+f = \frac{m4F}{3m} $
$ f = \frac{4}{3}F -F = \frac{F}{3}$