If the error in measurement of radius of a sphere is 2%, the percentage error in the calculated volume of the sphere will be: MCQ with Answer and Explanation

Question

If the error in measurement of radius of a sphere is 2%, the percentage error in the calculated volume of the sphere will be:

A. 2%

B. 8%

C. 6%

D. 4%

Answer: Option C

Solution (By JKSSB Mock Tests)

Volume of sphere V = (4/3)πr³. For error propagation, percentage error in V = 3 × (percentage error in r). Given error in r is 2%, so error in V = 3 × 2% = 6%. This follows the power rule: if Q = xⁿ, then % error in Q = |n| × % error in x. This principle is crucial for experimental error analysis. Exam tip: Remember that volume depends on cube of radius, so errors amplify threefold. This type of question tests understanding of error propagation in derived quantities.

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Question #1

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A capillary tube is dipped in water and the water rises to a height 'h'. If the experiment is performed in a freely falling elevator, the water column in the tube will:

A. Rise to height 2h

B. Rise to the full length of the capillary tube

C. Rise to height h

D. Not rise at all

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Correct Answer: Option B

Explanation:
The height of capillary rise is given by Jurin's law: h = 2Tcos(theta) / (rrhog). In a freely falling elevator, the effective acceleration due to gravity (g') is zero (weightlessness). As effective g approaches zero, the theoretical height h approaches infinity. In reality, the water will rise to the very top of the tube, regardless of its length, but will not overflow.

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Question #2

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A projectile is launched at 30° with speed 20 m/s. Horizontal range is: (g=10 m/s²)

A. 20 m

B. 20√3 m

C. 40 m

D. 10√3 m

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Correct Answer: Option B

Explanation:
Range R = u²sin(2θ)/g = (20)²×sin(60°)/10 = 400×(√3/2)/10 = 20√3 m. Formula applies for level ground projection. Memory tip: sin(2θ) for θ=30° is sin60°=√3/2. Standard projectile calculation frequently appearing in competitive exams with trigonometric values.

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