JEE Physics 2024 Question with Solution

Given: All surfaces are frictionless, and the pulleys and string are light. The required quantity is the acceleration of the block of mass $2 \, \text{kg}$.

Find: Acceleration of the $2 \, \text{kg}$ block.

The solution states that the correct option is B and concludes that the acceleration is $g/3$.

From the extracted working:

$$2a = g \sin(30^\circ) = \frac{g}{2}$$

and for the other mass,

$$4a = 2g \Rightarrow a = \frac{g}{3}$$

Thus, the acceleration of the block of mass $2 \, \text{kg}$ is $g/3$.

Therefore, the correct option is B.

Given: The system is frictionless and uses light pulleys and string.

Find: The acceleration of the $2 \, \text{kg}$ block.

The first solution passage says that for the $2 \, \text{kg}$ block, using Newton's second law,

$$T = 2a$$

It then mentions force balance relations in the pulley system and concludes that the acceleration should be $g/3$.

The second approach explicitly provides:

$$2a = g \sin(30^\circ) = \frac{g}{2}$$

and then states for the $4 \, \text{kg}$ mass,

$$4a = 2g \Rightarrow a = \frac{g}{3}$$

Although the intermediate equations in the solution are not fully consistent, the solution clearly identifies option B and concludes the acceleration as $g/3$.

Therefore, the acceleration is $g/3$ and the correct option is B.