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A broad vessel, with a square base of edge a = 10 cm is separated into two halves A and B, by a smooth vertical piston. A spring of spring constant k = 1500 N/m is filled across the compartment A and the compartment B is filled with water to a height 20 cm. Find the compression in the spring.

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a

1.3 cm

b

2.1 cm

c

3.9 cm

d

0.07 cm

answer is A.

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Detailed Solution

The force exerted on the spring, via the piston by water = (pressure at centroid of the piston) x (area of the piston)= (ρgh2)(ah)F = 1×1000×2022× 10 = 2× 105 dyneNow, if x cm be the compression of the springThen for equilibrium F = Kx.2×106 = 1500×103dynecm×x cmx = 2015 = 1.3 cm.

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A broad vessel, with a square base of edge a = 10 cm is separated into two halves A and B, by a smooth vertical piston. A spring of spring constant k = 1500 N/m is filled across the compartment A and the compartment B is filled with water to a height 20 cm. Find the compression in the spring.