A broad vessel, with a square base of edge `s = 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.

Options

A. 1.3 cm
B. 2.1 cm
C. 3.9 cm
D. 0.07 cm

Answer

A

Explanation

(a) The force exerted on the spring, via the piston be water = (pressure at centroid of the pistion) xx (area of the pistion)
`=(rho g (h)/(2)) ((ah))`
`F = 1 xx 1000 xx (20^2)/(2) xx10 = 2 xx 10^5 dyne`
Now, if x cm be the comperession of the spring Then for equilibrium F = Kx.
` 2 xx 10^6 = 1500 xx 10^3 (dyne)/(cm) xx x cm`
x = 20//15 =1.3 cm