Question

A system is shown in the figure. A man standing on the block is pulling the rope. If the man pulls $2m$ of the rope in each second, then the velocity of the block will be
[Assume that the block does not rotate and rope is inextensible.]

• A. $3m/s$
• B. $2m/s$
• C. $\frac{1}{2}m/s$
• D. $1m/s$

Answer 1

The correct option is D $1m/s$

Let $V$ be the velocity of the block.
Velocity at which rope is pulled $=2m/s$

Since the string is extensible,
$l_1+l_2+l_3+l_4=\text{constant}$
Differentiating w.r.t time, we get equation in the form of velocity,
$\frac{d{l}_1}{dt}+\frac{d{l}_2}{dt}+\frac{d{l}_3}{dt}+\frac{d{l}_4}{dt}=0$
$-V-V+0+2=0$
$V=1m/s$