Question

Find the acceleration of block $C$ i.e. $a_C$ in the shown figure.

• A. $a_C=6{\text{m/s}}^2$, upwards
• B. $a_C=4{\text{m/s}}^2$, upwards
• C. $a_C=5{\text{m/s}}^2$, upwards
• D. $a_C=2{\text{m/s}}^2$, upwards

Answer 1

The correct option is A $a_C=6{\text{m/s}}^2$, upwards

Let us assume that the acceleration of block $C$ be upwards and taking upward positive we have
From the string constraints,
$a_{P2}=2\sqrt{3}\cos {30}^{\circ }=3{\text{m/s}}^2$, upwards
Now, for pulley $P2:$
$a_{P2}=\frac{a_C+a_A}{2}\Rightarrow 3=\frac{a_C+0}{2}\Rightarrow a_C=6{\text{m/s}}^2$
Hence, the acceleration of the block $C$ is $a_C=6{\text{m/s}}^2$, upwards.