MHT CET · Physics · Laws of Motion

Two identical blocks each of mass ' \(M\) ' attached to the ends of a massless inextensible string which passes over a pulley with a fixed axis as shown below. A small mass ' \(m\) ' is now placed on the block B. The acceleration with which the two blocks move together is
[ \(\mathrm{g}=\) gravitational acceleration]

A \(\frac{\mathrm{mg}}{2 \mathrm{M}+\mathrm{m}}\)
B \(\frac{\mathrm{Mg}}{\mathrm{M}+2 \mathrm{~m}}\)
C \(\frac{\mathrm{Mg}}{2 \mathrm{M}+\mathrm{m}}\)
D \(\frac{m g}{M+2 m}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{\mathrm{mg}}{2 \mathrm{M}+\mathrm{m}}\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned}
& (\mathrm{M}+\mathrm{m}) \mathrm{g}-\mathrm{T}=(\mathrm{M}+\mathrm{m}) \mathrm{a} \\
& \mathrm{~T}-\mathrm{Mg}=\mathrm{Ma}
\end{aligned}\)
Adding the above equations,
\((\mathrm{M}+\mathrm{m}) \mathrm{g}-\mathrm{Mg}=(2 \mathrm{M}+\mathrm{m}) \mathrm{a}\)
\(\therefore \quad a=\frac{m g}{(2 M+m)}\)

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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