Question

In the given pulley arrangement, Block $A$ is going downward with speed $10m/s$, B is going upward with speed $2m/s$, C is going downward with speed $4m/s$. Find speed of Block D.
(All speed are w.r.t ground)

• A. $4m/s$ (Downward)
• B. $12m/s$ (Downward)
• C. $4m/s$ (Upward)
• D. $12m/s$ (Upward)

Answer 1

The correct option is D $12m/s$ (Upward)

$V_A=-10m/s$ $V_C=-4m/s$

$V_B=+2m/s$ $V_D=?$

$V_{P_1}=\frac{V_A+V_B}{2}$

$V_{P_1}=\frac{-10+2}{2}$

$V_{P_1}=-4m/s$ (-ve means downward)

Now

$\left(V_{P_1}\right)=-\left(V_{P_2}\right)$

$V_{P_2}=4m/s$
Now for $P_2$

$V_{P_2}=\frac{V_C+V_D}{2}$
$+4=\frac{-4+V_D}{2}$

$V_D=8+4$

$V_D=12m/s$ (+ve means upward)