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. 6%

B. 2%

C. 8%

D. 4%

Answer: Option A

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

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A passenger in a moving train tosses a coin which falls behind him. This shows that the motion of the train is:

A. Retarded

B. Uniform

C. Accelerated

D. Along a circular track

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Correct Answer: Option C

Explanation:
When the coin is tossed, it moves forward with the initial velocity of the train due to inertia of motion. If the train accelerates during the time the coin is in the air, the train moves faster and travels a greater distance horizontally than the coin. Thus, the coin falls behind the passenger.

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Question #2

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According to the Universal Law of Gravitation, the force of attraction between two bodies is inversely proportional to:

A. The sum of their masses.

B. The distance between them.

C. The product of their masses.

D. The square of the distance between their centers.

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Correct Answer: Option D

Explanation:
Newton's Law of Universal Gravitation states that the gravitational force (F) between two point masses is directly proportional to the product of their masses (m1 × m2) and inversely proportional to the square of the distance (r²) between their centers. The mathematical formula is F = G(m1m2)/r².

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