CUET · PHYSICS · PYQ PAPER 2025

Three concentric metallic spherical shells of radii \( R, 2R \), and \( 3R \) are given charges \( Q_1, Q_2 \) and \( Q_3 \), respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells \( Q_1 : Q_2 : Q_3 \) is:

A \(1: 2: 3\)
B \(1: 4: 9\)
C \(1: 3: 5\)
D \(1: 8: 18\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(1: 3: 5\)

Step-by-step Solution

Detailed explanation

\(\sigma_1 = \frac{Q_1}{4\pi R^2}\) \(\sigma_2 = \frac{Q_1+Q_2}{4\pi (2R)^2} = \frac{Q_1+Q_2}{16\pi R^2}\) \(\sigma_3 = \frac{Q_1+Q_2+Q_3}{4\pi (3R)^2} = \frac{Q_1+Q_2+Q_3}{36\pi R^2}\) Since \(\sigma_1 = \sigma_2 = \sigma_3 = \sigma\): \(Q_1 = 4\pi R^2 \sigma\)…

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

Match List-I with List-I

List-I	List-II
A. Electric field outside a uniformly charged thin spherical shell	(I) zero
B. Electric field inside a uniformly charged thin spherical shell	(II) \(\frac{\lambda}{2 \pi \epsilon_0 r} \vec{n}\)
C. Electric field due to an infinitely long straight uniformly charged wire	(III) \(\frac{\sigma}{2 \epsilon_0} \vec{n}\)
D. Electric field due to a uniformly charged infinite plane sheet	(IV) \(\frac{k q}{r^2} \vec{r}\)

Choose the correct answer from the options given below:

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