AP EAMCET · PHYSICS · Oscillations

A solid sphere of radius $R$ carries a positive charge $Q$ distributed uniformly throughout its volume. A very thin hole is drilled through it's center. A particle of mass $m$ and charge $- q$ performs simple harmonic motion about the center of the sphere in this hole. The frequency of oscillation is

A $\frac{1}{2 π} {[\frac{Q q}{4 π ε_{0} R^{3} m}]}^{\frac{1}{2}}$
B $\frac{1}{2 π} {[\frac{Q q}{4 π ε_{0} R^{2} m}]}^{\frac{1}{2}}$
C $\frac{1}{2 π} \frac{Q}{{[4 π ε_{0} m R^{3}]}^{- \frac{1}{2}}}$
D $\frac{1}{2 π} {[\frac{Q q}{4 π ε_{0} m R}]}^{\frac{1}{2}}$

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Answer & Solution

Correct Answer

(A) $\frac{1}{2 π} {[\frac{Q q}{4 π ε_{0} R^{3} m}]}^{\frac{1}{2}}$

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Detailed explanation

Electric field inside a uniformly charged solid sphere is given by, E=Qr4πε0R3. Therefore, the force on the negative charge -q at distance r from the centre will be F=-Qrq4πε0R3. Comparing it with F=-kx, k=Qq4πε0R3. Now the frequency of the…

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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A solid sphere of radius R carries a positive charge Q distributed uniformly throughout its volume. A very thin hole is drilled through it's center. A particle of mass m and charge -q performs simple harmonic motion about the center of the sphere in this hole. The frequency of oscillation is

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