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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2.1 cm

3.9 cm

1.3 cm

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)

= $(ρg \frac{h}{2}) (ah)$
F = $1 \times 1000 \times \frac{20^{2}}{2} \times 10$ = 2 $\times 10^{5} dyne$
Now, if x cm be the compression of the spring
Then for equilibrium F = Kx.

$2 \times 10^{6} = 1500 \times 10^{3} \frac{dyne}{cm} \times x cm$

$x = \frac{20}{15} = 1.3 cm .$

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