Question

System is shown in the figure and man is pulling the rope from both sides with constant speed $‘u^{\prime }$. Then what will be the velocity of the block, if the rope is inextensible?

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

Answer 1

The correct option is B $\frac{u}{2}$

Velocities of pulley $P_1$ and block $M$ are assumed to be upwards. The velocities of points $A,B,C,E,F$ and $G$ are each equal to $v$ as they are connected to $M$.
$l_0+l_1=\text{constant}\Rightarrow u-v_{p_1}=0\Rightarrow v_{p_1}=u$ ... (i)
$l_2+l_3+l_4+l_5+l_6+l_7+l_8+l_9+l_{10}=\text{constant}$
Differentiating w.r.t time, we get equation in the form of velocity i.e.
$\Rightarrow v_{P_1}+v_{P_1}-v-v-v+0+0-v-v-v+u=0$
$\Rightarrow 2v_{P_1}-6v+u=0$ ... (ii)
From (i) and (ii)
$3u=6v\Rightarrow v=\frac{u}{2}\uparrow$