First slide

Fluid statics

Question

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.

Moderate

A

1.3 cm
B

2.1 cm
C

3.9 cm
D

0.07 cm

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.
$2 \times 10^{6} = 1500 \times 10^{3} \frac{dyne}{cm} \times x cm$
$x = \frac{20}{15} = 1.3 cm .$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App