Question

A solid sphere of mass $m$ is lying at rest on a rough horizontal surface. The coefficient of friction between ground and sphere is $\mu$. The maximum value of $F$, so that sphere will not slip, is equal to

• A. $7\mu mg/2$
• B. $4\mu mg/5$
• C. $5\mu mg/5$
• D. $7\mu mg/5$

Answer 1

The correct option is A $7\mu mg/2$

$\begin{array}{c}Ff=Macm.......\left(1\right)\\ f_e=I\alpha \\ f=\frac{2}{5}M{R}^2.\frac{\alpha }{R}\\ f=\frac{2}{5}M{a}_{cm}.......\left(2\right)\left[a_{cm}=Rdforrolling\right]\\ \mu mg\ge \frac{2}{5}m{a}_{cm}\\ a_{cm}\le \frac{5}{2}\mu g\\ from\left(1\right)and\left(2\right)\\ F=M\left[1+\frac{2}{5}\right]a_{cm}\\ =\frac{7}{5}M{a}_{cm}\\ F_{max}=\frac{7}{5}M\frac{5}{2}\mu g\\ =\frac{7}{2}M\mu g\\ Hence,\\ optionAiscorrectanswer.\end{array}$