Question

If block $A$ has a velocity of $0.6\text{m/s}$ to the right, determine the velocity of block $B$. Assume that the surface is frictionless and the string is inextensible.

• A. $1.8\text{m/s}$ in downward direction
• B. $1.8\text{m/s}$ in upward direction
• C. $0.6\text{m/s}$ in downward direction
• D. $0.6\text{m/s}$ in upward direction

Answer 1

The correct option is A $1.8\text{m/s}$ in downward direction

Let $V_P$ and $V$ be the velocity of pulley P and block B respectively.
From length constraint,
$2l_1+l_2=L$
Differentiating w.r.t time, we get the equation in the form of velocity i.e.
$\Rightarrow \frac{2d{l}_1}{dt}+\frac{d{l}_2}{dt}=0$
$-2V_P+(V-V_P)=0$
$3V_P=V$
Since pulley P is fixed to block A, therefore $V_P=0.6\text{m/s}$
$\Rightarrow V=3\times 0.6=1.8\text{m/s}$