Question

If the pulley is pulled down with a force of $120\text{N}$ as shown in figure. The acceleration of $8\text{kg}$ block would be:
(All pulleys are light and frictionless, string is massless and inextensible)
(Take $g=10{\text{m/s}}^2$)

• A. $0$
• B. $5{\text{m/s}}^2$
• C. $10{\text{m/s}}^2$
• D. $4{\text{m/s}}^2$

Answer 1

The correct option is B $5{\text{m/s}}^2$

FBD of pulley $P_1:$


$2T=120$ (massless pulley)

$\Rightarrow T=60\text{N}$

Let $a$ be the acceleration of the block.

Since a single string is connected throughout. So, F.B.D of $8\text{kg}$ block and pulley $P_2$ will be



From FBD of block, we get

$F_{net}=ma$

$\Rightarrow 2T-8g=8a$

$\Rightarrow 120-80=8a$

$\therefore a=\frac{40}{8}=5{\text{m/s}}^2$

Hence, option $\left(b\right)$ is correct.