Question

In the figure shown below, acceleration of block $A$ is $1{\text{m/s}}^2$ upwards, acceleration of block $B$ is $7{\text{m/s}}^2$ upwards and acceleration of block $C$ is $2{\text{m/s}}^2$ upwards. Then what will be the acceleration of block $D$? Assume that the pulleys are frictionless and strings are inextensible.

• A. $7{\text{m/s}}^2$ upwards
• B. $2{\text{m/s}}^2$ downwards
• C. $10{\text{m/s}}^2$ downwards
• D. $8{\text{m/s}}^2$ upwards

Answer 1

The correct option is C $10{\text{m/s}}^2$ downwards


Taking upward acceleration positive and downward negative.
Let the acceleration of pulley P and Q be $a_P$ and $a_Q$ respectively.
Acceleration of block A, $a_A=1m/s^2$
Acceleration of block B, $a_B=7m/s^2$
Acceleration of block C, $a_C=2m/s^2$
Acceleration of block D $=a_D$
Now $a_P=\frac{a_A+a_B}{2}$
$a_P=\frac{1+7}{2}=4m/s^2\text{Upwards}$
Since string is inextensible, length remains same.
Therefore acceleration of pulley Q, $a_Q=-4m/s^2$
Also $a_Q=\frac{a_C+a_D}{2}$
$\Rightarrow -4=\frac{2+a_D}{2}$
$\Rightarrow a_D=-10m/s^2$
Since acceleration is negative, therefore downwards.