MHT CET · Physics · Oscillations

Two bodies A and B of equal mass are suspended from two separate massless springs of spring constants \(\mathrm{K}_1\) and \(\mathrm{K}_2\) respectively. The two bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitude of B to that of A is

A \(\frac{\mathrm{K}_1}{\mathrm{~K}_2}\)
B \(\frac{\mathrm{K}_2}{\mathrm{~K}_1}\)
C \(\sqrt{\frac{\mathrm{K}_1}{\mathrm{~K}_2}}\)
D \(\sqrt{\frac{\mathrm{K}_2}{\mathrm{~K}_1}}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\sqrt{\frac{\mathrm{K}_1}{\mathrm{~K}_2}}\)

Step-by-step Solution

Detailed explanation

If the maximum velocities of the bodies are equal, then their total energy would also be the same. If \(\mathrm{A}_1, \mathrm{~A}_2\) are the amplitudes of A and B respectively, then
\(\begin{aligned}
& \frac{1}{2} \mathrm{~K}_1 \mathrm{~A}_1^2=\frac{1}{2} \mathrm{~K}_2 \mathrm{~A}_2^2 \\
\therefore \quad & \frac{\mathrm{~A}_2}{\mathrm{~A}_1}=\sqrt{\frac{\mathrm{K}_1}{\mathrm{~K}_2}}
\end{aligned}\)

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.

Same subject

Explore more questions on app

From MHT CET

Explore more questions on app