Question

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

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

Answer 1

Answer: (D)

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