Question

A disc of mass $M$ & radius $R$ is placed a rough horizontal surface with its axis horizontal. A light rod of length '$2R$' is fixed to the disc at point '$A$' as shown in figure and a force $\frac{3}{2}Mg$ is applied at the other end. If disc starts to roll without slipping find the value of " $10\times {\mu }_{\min }"$ where ${\mu }_{\min }$ is minimum coefficient of friction $b/w$ disc & horizontal surface required for pure rolling-

Answer 1

Answer: 8.00

$\tau$ at $P=\frac{3Mg}{2}\times 2R$
$=3MgR$
$3MgR=\left(\frac{M{R}^2}{2}+M{R}^2\right)\alpha$
$\alpha =\frac{2MgR}{M{R}^2}$
$\alpha =\frac{2g}{R}$
$a-\alpha R=0$
$a=2g$
$f=Ma$
$f=2Mg$
$\frac{3}{2}Mg+Mg=N$
$N=\frac{5}{2}Mg$
$f\le \mu N$
$2Mg\le \mu \frac{5}{2}Mg$
$\mu \ge \frac{4}{5}$
${\mu }_{\min }=\frac{4}{5}$
$10\times {\mu }_{\min }\Rightarrow 10\times \frac{4}{5}$
$\Rightarrow 8$