Question

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

• A. $6m/s\uparrow$
• B. $6m/s\downarrow$
• C. $4m/s\uparrow$
• D. $8m/s\uparrow$

Answer 1

The correct option is A $6m/s\uparrow$

Given $V_L=$ velocity of lift =$2m{s}^{-1}$ up.

$V_{string}=2m{s}^{-1}$ (i.e $-\frac{dl}{dt}$ because length is decreasing).

$V_A=2m{s}^{-1}$ down

Now from figure, it is clear that ,

$y=x-(l-x)$

$y=2x-l$

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 = $6m{s}^{-1}$

Option $A$ is correct.