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Q.

A cylindrical block of area of cross-section A and of material of density $ρ$ is placed in a liquid of density one-third of density of block. The block compresses a spring and compression in the spring is one-third of the length of the block. If acceleration due to gravity is g, the spring constant of the spring is

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a

$2 ρ Ag$

b

$ρ Ag / 3$

c

$2 ρ Ag / 3$

d

$ρ A g$

answer is B.

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Detailed Solution

Question Image

W = Weight
U = Upthrust
S = Spring force
U + S = W

$(Ah) \frac{ρ}{3} g + k (\frac{h}{3}) = (Ah) ρ g$

$k = 2 ρ Ag$

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A cylindrical block of area of cross-section A and of material of density ρ is placed in a liquid of density one-third of density of block. The block compresses a spring and compression in the spring is one-third of the length of the block. If acceleration due to gravity is g, the spring constant of the spring is