Question

In the given constraint, if the string is inextensible and pulley is frictionless, then magnitude of velocity of block $A$ $\left(V_A\right)$ is

• A. $10\text{m/s}$
• B. $20\text{m/s}$
• C. $15\text{m/s}$
• D. $5\text{m/s}$

Answer 1

The correct option is B $20\text{m/s}$


Velocity of pulley, $V_P=\frac{V_A+V_B}{2}$
Putting $V_P=10\text{m/s},V_B=0,$
we get
$V_A=20\text{m/s}$ (upward direction)

Alternative solution:

Since the string is inextensible, therefore
$X_p+(X_P-X_A)$ = length of string
$\Rightarrow 2X_p-X_A=L$
Differentiating w.r.t time, we get equation in terms of velocity i.e.
$\Rightarrow 2V_p-V_A=0$
$\Rightarrow V_A=2V_P$
$V_A=2\left(10\right)=20\text{m/s}$