MHT CET · Physics · Laws of Motion

A body of mass 200 gram is tied to a spring of spring constant \(12.5 \mathrm{~N} / \mathrm{m}\), while other end of spring is fixed at point ' \(\mathrm{O}\) '. If the body moves about ' \(\mathrm{O}\) ' in a circular path on a smooth horizontal surface with constant angular speed \(5 \mathrm{rad} / \mathrm{s}\) then the ratio of extension in the spring to its natural length will be

A \(1: 2\)
B \(1:1\)
C \(2:3\)
D \(2:5\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(2:3\)

Step-by-step Solution

Detailed explanation

Let the normal length be \(\mathrm{L}\) and the extension be \(\mathrm{x}\).
\(\therefore \quad\) Restoring Force \(=\) Centripetal Force
\(\begin{aligned}
& \mathrm{kx}=\mathrm{m}(\mathrm{L}+\mathrm{x}) \omega^2 \\
& 12.5 \mathrm{x}=0.2(\mathrm{~L}+\mathrm{x}) 25 \quad \ldots(\because \omega=5 \mathrm{rad} / \mathrm{s})
\end{aligned}\)
\(\begin{aligned} & 12.5 x=5(L+x) \\ & 7.5 x=5 L \\ \therefore \quad & \frac{x}{L}=\frac{5}{7.5}=\frac{2}{3}=2: 3\end{aligned}\)

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.

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