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Question

If W1 and W2 are weights of two solid iron balls of radii ½ metre and 1/3 metre respectively, then which one of the following is equal to W1 : W2?

A 8: 27 Correct Answer Incorrect Answer
B 27: 8 Correct Answer Incorrect Answer
C 4:16 Correct Answer Incorrect Answer
D 16:4 Correct Answer Incorrect Answer

Solution

Weight = Volume x Density Both balls are of same material, hence Weight ∝ Volume. Volume of ball = (4/3)πR³ R = Radius of the ball W ∝ (4/3)πR³ As (4/3)π are constant => W ∝ R³ => W₁ ∝ (1/2)³ => W₂ ∝ (1/3)³ => W₁ / W₂ = (1/2)³ / (1/3)³ => W₁ / W₂ = (3/2)³ => W₁ / W₂ = 27/8 => W₁ : W₂ = 27 : 8

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