Question

The diameter of the press (load) piston of a hydraulic lift is eight times the diameter of the pump (effort) piston. If a force 'F' newton is applied on the effort piston, then the maximum weight that can be lifted by press piston in terms of 'F' is ______
(A) $\text{16F}$
(B) $\text{50F}$
(C) $64F$
(D) $\text{32F}$

Answer 1

Hint A hydraulic lift is a type of machine that uses a hydraulic apparatus to lift or move objects using the force created when pressure is exerted on liquid in a piston. Force then produces "lift" and "work." Hydraulic lifts work on a basic principle: to go up, a pump pushes oil into the cylinder, pushing the piston (which pushes the lift car) up. To go down, the valve opens and oil is allowed to flow back into the reservoir, and is pushed back using the gravitational force of the lift car.

Complete step by step answerLet the radius of the effort piston be x.
Hence, from the question, we can determine that the radius of the piston on load is 8x.
The area on the load piston is 64 times that from the effort piston.
We know that,
$P=\dfrac{F}{A}$
Let the force applied on effort piston = F
Let the maximum force applied by load piston = ${{F}_{1}}$
Therefore,
$\dfrac{F}{{{x}^{2}}}=\dfrac{{{F}_{1}}}{64{{x}^{2}}}$
$\therefore {{F}_{1}}=64F$

Hence, the correct answer is Option C.

Note: Hydraulic lifts are used in a variety of different applications. They can be found in automotive, shipping, construction, waste removal, mining, and retail industries as they're an effective means of raising and lowering people, goods, and equipment. The basic principle behind any hydraulic system is very simple - pressure applied anywhere to a body of fluid causes a force to be transmitted equally in all directions, with the force acting at right angles to any surface in contact with the fluid. This is known as Pascal's Law.