Question

In the figure shown the velocity of lift is $2m{s}^{-1}$ upwards while the string is winding on the motor shaft with velocity $2m{s}^{-1}$ and block $A$ is moving downwards with a velocity of $2m{s}^{-1}$ , then find out the velocity of block $B$ .

• A. $2m{s}^{-1}\uparrow$
• B. $2m{s}^{-1}\downarrow$
• C. $4m{s}^{-1}\downarrow$
• D. $6m{s}^{-1}\uparrow$

Answer 1

Answer: (D)

Given $V_L=$ velocity of lift $=2m{s}^{-1}$ up.
$V_{\text{string }}=2m{s}^{-1}$ (i.e $-\frac{dl}{dt}$ because length is decreasing).
$V_A=2m{s}^{-1}$ down
Now from figure, it is clear that,
$y=x-(1-x)$
$y=2x-1$
On Differentiating,
$\frac{dy}{dt}=2\frac{dx}{dt}-\frac{dl}{dt}$
$\frac{dy}{dt}=2\times 2-(-2)$
$\frac{dy}{dt}=6m{s}^{-1}$
i.e velocity of block $B=6m{s}^{-1}$