Question

Block $B$ of mass $100\text{kg}$ rests on a rough surface of friction coefficient $\mu =\frac{1}{3}$. A rope is tied to block $B$ as shown in figure. The maximum acceleration with which boy $A$ of $25\text{kg}$ can climb on rope without making block move is ($g=10m{s}^{-2}$)

• A. $\frac{4g}{3}$
• B. $\frac{g}{3}$
• C. $\frac{g}{2}$
• D. $\frac{3g}{4}$

Answer 1

The correct option is B $\frac{g}{3}$


$T\cos {37}^{\circ }=f$
$N+T\sin {37}^{\circ }=mg$
$\therefore N=100g-T\sin {37}^{\circ }=100g-\frac{3T}{5}$
and, $T\cos {37}^{\circ }=\mu N$
$T\cos {37}^{\circ }=\mu (100g-\frac{3T}{5})$
On solving, $T=\frac{1000}{3}\text{N}(\mu =\frac{1}{3})$
$\therefore T-Mg=M{a}_{\text{max}}$
$\frac{1000}{3}-250=25\times a_{\text{max}}$
$a_{\text{max}}=\frac{10}{3}{\text{m/s}}^2$