Question

Block $B$ of mass $100kg$ rests on a rough surface of friction coefficient $\mu =1/3$. A rope is tied to block $B$ as shown in figure. The maximum acceleration with which boy $A$ of $25kg$ can climbs on rope without making block move is

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

Answer 1

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

$N=Mg-T\sin {37}^{\circ }=100\times 10-T.\frac{3}{5}$

Ffrictional force, $f=\mu N$

$T_{max}$ for which block doesn't move then,

$T\cos {37}^{\circ }=f=\mu N$

$T.\frac{4}{5}=\frac{1}{3}(1000-\frac{3T}{5})$

$\frac{4T}{5}+\frac{T}{5}=\frac{1000}{3}$

$T=\frac{1000}{3}$

Now, taking body into account ;

$T-m_{2}g=ma$

$\frac{1000}{3}-25\times 10=25a$

$a=\frac{1000-750}{3}=\frac{250}{3\times 25}=\frac{10}{3}or\frac{g}{3}$