Physics - NLM Question with Solution | TestHub

For the particle to undergo complete vertical circular motion, its speed at the lowest point should be at least $v=\sqrt{5gr}$. Also, the tension in the string is maximum when the particle is at the lowest point. The tension at the lowest position of the particle is

$T=mg+\frac{m{v}^2}{r}$

$\Rightarrow T=mg+\frac{m\left(5gr\right)}{r}=6mg$

The friction force acting on the block should be able to balance the maximum tension.

$f=T=6mg$

$f=6mg\le \mu Mg$

$\Rightarrow M\ge \frac{6m}{{\displaystyle \raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}=9m$

$M_{\min }=9m$