If the random error in measurement of radius of a sphere is 2%, the error in volume is MCQ with Answer and Explanation

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If the random error in measurement of radius of a sphere is 2%, the error in volume is

A. 4%

B. 6%

C. 2%

D. 8%

Answer: Option B

Solution (By JKSSB Mock Tests)

Volume V = (4/3)πr³. Fractional error ΔV/V = 3 Δr/r. Percentage error = 3 × 2% = 6%. Important for error analysis in competitive exams.

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Question #1

The speed of sound in air at 0°C is 331 m/s. At 22°C, approximately

A. 343 m/s

B. 350 m/s

C. 331 m/s

D. 360 m/s

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Correct Answer: Option A

Explanation:
v ≈ 331 + 0.6×T(°C) = 331 + 0.6×22 = 331+13.2 = 344.2 m/s, nearest 343 m/s.

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Question #2

A spring of spring constant k is cut into four equal parts. The spring constant of each part is

A. k/4

B. 2k

C. 4k

D. k

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Correct Answer: Option C

Explanation:
For a spring, k ∝ 1/length. So quarter length has 4 times k. Each part has constant 4k.

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Question #3

Gravitational force between two masses varies with distance r as:

A. r

B. 1/r²

C. r²

D. 1/r

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Correct Answer: Option B

Explanation:
Newton's law: F = Gm₁m₂/r² ⇒ F ∝ 1/r². Inverse square law fundamental to gravitation, electrostatics, and radiation intensity. Memory aid: 'Gravity weakens with square of distance; double distance ⇒ force becomes 1/4'. Core concept frequently tested to verify understanding of fundamental force laws in competitive exams.

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