Question

The area of cross-section of the two arms of a hydraulic press are 1 $c{m}^2$ and 10 $c{m}^2$ respectively (figure). A force of 50 N is applied on the water in the thicker arm. What force should be applied on the water in the thinner arm so that the water may remain in equilibrium?

• A. 5 N
• B. 10 N
• C. 25 N
• D. 50 N

Answer 1

The correct option is A 5 N

Answer is A.
In equilibrium, the pressures at the two surfaces should be equal as they lie in the same horizontal level. If the atmospheric pressure is P and a force F is applied to maintain the equilibrium, the pressures are
$P_0+\frac{50N}{10c{m}^2}and{P}_0+\frac{F}{1c{m}^2}$
This givens F = 5 N.
Hence, force that should be applied on the water in the thinner arm so that the water may remain in equilibrium is 5 N.