Logo
Jeeify
MCQEasyJEE 2023Capacitors & Dielectrics

JEE Physics 2023 Question with Solution

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one.

Reason R: Capacitance of metallic spheres depend on the radii of spheres.

In the light of the above statements, choose the correct answer from the options given below.

  • A

    A is false but R is true

  • B

    Both A and R are true and R is the correct explanation of A

  • C

    A is true but R is false

  • D

    Both A and R are true but R is not the correct explanation of A

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: Two metallic spheres are at the same potential and have the same radius. One sphere is hollow and the other is solid.

Find: Whether Assertion A and Reason R are true, and which option is correct.

For a conducting sphere, the potential is

V=KQRV = \frac{KQ}{R}

where VV is potential, QQ is charge, and RR is radius.

If both spheres have the same potential and the same radius, then

KQ1R1=KQ2R2\frac{KQ_1}{R_1} = \frac{KQ_2}{R_2}

With R1=R2R_1 = R_2, we get

Q1=Q2Q_1 = Q_2

So the statement that the solid sphere will have lower charge than the hollow sphere is false.

Now, the capacitance of an isolated metallic sphere is

C=4πϵ0RC = 4\pi \epsilon_0 R

Thus, capacitance depends only on the radius of the sphere, not on whether it is hollow or solid. Therefore, Reason R is true.

The solution states "The Correct Option is D", but its own working concludes that Assertion A is false and Reason R is true. That conclusion matches option A, not option D.

Therefore, Assertion A is false but Reason R is true. The correct option is A.

Common mistakes

  • Assuming a solid metallic sphere and a hollow metallic sphere have different potentials or charge relations merely because of material distribution is incorrect. For conductors, external potential depends on total charge and radius. Use the conducting sphere formula based on radius, not interior filling.

  • Confusing capacitance with volume is wrong. Capacitance of a metallic sphere depends only on its radius, not on whether the sphere is solid or hollow. Always recall C=4πϵ0RC = 4\pi \epsilon_0 R for an isolated sphere.

  • Trusting the listed option letter without checking the actual solution logic can lead to an incorrect answer. Here the written conclusion in words matches option A, even though the page also incorrectly labels the option as D. Verify the reasoning before selecting.

Practice more Capacitors & Dielectrics questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step — free to start.

Start free trialMore on Capacitors & Dielectrics

Related questions