Question

What will be the velocity of block A in the arrangement shown ?

• A. $60m/s$
• B. $120m/s$
• C. $140m/s$
• D. $200m/s$

Answer 1

The correct option is C $140m/s$

Let the downward velocity be negative and upward velocity be postive.
Pulley (1) is fixed
So $V_B=V_{plank}=-20m/s$
and $V_C=20m/s$

Considering pulley (2), we can say
that $V_D=V_C=20m/s$
and $V_E=-20m/s$ (since the string is connected to the plank)

$V_D=\frac{V_E+V_G}{2}$
$\Rightarrow 20=\frac{-20+V_G}{2}$
$\Rightarrow V_G=60m/s$

Now considering pulley (3)

$V_I=-20m/s$ (connected to the plank)
and $V_H=V_G=60m/s$

$V_H=\frac{V_I+V_J}{2}$
$\Rightarrow 60=\frac{-20+V_J}{2}$
$\Rightarrow 120=V_J-20$
$\Rightarrow V_J=140m/s$

Therefore velocity of block A $V_A=V_J=140m/s$