If W1 and W2 are weights of two solid iron balls of radii 1/2 metre and 1/3 metre respectively, then which one of the following is equal to W:W2?
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Given : W₁ and W₂ are weights of two solid iron balls of radii 1/2 meter and 1/3 meter respectively,
To Find: W₁ : W₂
Solution:
Weight = Volume * 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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