WBJEE · Physics · Laws of Motion

Two weights of the mass \(m_{1}\) and \(m_{2}\left(>m_{1}\right)\) are joined by an inextensible string of negligible mass passing over a fixed frictionless pulley. The magnitude of the acceleration of the loads is

A \(g\)
B \(\frac{m_{2}-m_{1}}{m_{2}} g\)
C \(\frac{m_{1}}{m_{2}+m_{1}} g\)
D \(\frac{m_{2}-m_{1}}{m_{2}+m_{1}} g\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{m_{2}-m_{1}}{m_{2}+m_{1}} g\)

Step-by-step Solution

Detailed explanation

According to the question, we can draw the following diagram Here, \(T\) is the tension in the string. In equilibrium condition. For mass \(m_{1}, \quad T-m_{1} g=m_{1} a\)....(i) For mass \(m_{2}, \quad m_{2} g-T=m_{2} a\)....(ii) After adding Eqs. (i) and (ii), we get…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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