Assertion (A): The coefficient of volume expansion of a solid is approximately three times its coefficient of linear expansion. Reason (R): Volume is a three-dimensional property derived from cubing the linear dimension. MCQ with Answer and Explanation

Question

Assertion (A): The coefficient of volume expansion of a solid is approximately three times its coefficient of linear expansion. Reason (R): Volume is a three-dimensional property derived from cubing the linear dimension.

A. A is true but R is false.

B. A is false but R is true.

C. Both A and R are true but R is NOT the correct explanation of A.

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

Answer: Option D

Solution (By JKSSB Mock Tests)

The coefficient of linear expansion is alpha. A cube of side L has volume V = L^3. When heated, the new length is L(1+alphadT). The new volume is [L(1+alphadT)]^3. Expanding via binomial theorem and ignoring higher-order small terms gives V' = V(1 + 3alphadT). Thus, the volume expansion coefficient gamma is equal to 3alpha. Reason R correctly explains Assertion A.

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A particle covers half of its total distance with speed v1 and the rest half distance with speed v2. Its average speed during the complete journey is:

A. (v1^2 + v2^2) / (v1 + v2)

B. (v1 * v2) / (v1 + v2)

C. 2(v1 * v2) / (v1 + v2)

D. (v1 + v2) / 2

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Correct Answer: Option C

Explanation:
When equal distances are covered with different speeds v1 and v2, the average speed is not the arithmetic mean, but the harmonic mean of the two speeds. Total distance = 2x. Total time = (x/v1) + (x/v2). Average speed = Total Distance / Total Time = 2x / [x(1/v1 + 1/v2)] = 2v1v2 / (v1 + v2).

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Question #2

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The part of human eye that controls amount of light entering is

A. Lens

B. Iris

C. Cornea

D. Retina

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Correct Answer: Option B

Explanation:
Iris adjusts pupil size. In bright light pupil constricts, dim light dilates. Retina forms image. Cornea and lens focus. Eye is like camera.

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Question #3

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The instrument that converts mechanical energy into electrical energy is:

A. Galvanometer

B. Electric motor

C. Transformer

D. Generator

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Correct Answer: Option D

Explanation:
Generator converts mechanical energy (rotation) to electrical energy via electromagnetic induction. Motor does the reverse (electrical to mechanical). Transformer changes AC voltage levels; galvanometer detects small currents. Memory aid: 'Generator: motion ⇒ electricity; Motor: electricity ⇒ motion'. This principle-based question tests understanding of energy conversion devices, crucial for electromagnetism in competitive exams. Always link device function to underlying physics law: generator (Faraday's law), motor (Lorentz force).

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