Question

If block A starts from rest at $t=0$ & begins to move towards right with an acceleration of $2m/s^2$ & simultaneously bolck C moves towards right with constant velocity of $4m/s$. Speed of block B at $t=5s$ will be

• A. $2m/s$
• B. $3m/s$
• C. $4m/s$
• D. None

Answer 1

The correct option is B $3m/s$

Velocity of block A $=0+at=2t$
So from 0 to 2 seconds, block A's velocity will be less than block C's velocity of $4m/s$, therefore pulley 2 and block B will move up.

At 2 seconds, velocities of block A and C are equal and therefore pulley 2 and block B will be at rest and after $t=2s$, they start to move down


From the diagram, $l_1,l_2$ and $l_3$ are the segments of the string. Therefore at $t=5s$,
$l_1+2l_2+l_3=\text{constant}$
Differentiating w.r.t $t$, we get
$-v_1+2v_2+v_3=0$
($l_1$ is decreasing and $l_2$ and $l_3$ are increasing)
$\Rightarrow -(2\times 5)+2v_2+4=0$
$\Rightarrow 2v_2=6$
$\Rightarrow v_2=3m/s$ is the velocity of block B at $5s$