Question

A trolley of 10,000 kg is placed on a platform which is fixed to a press piston of a hydraulic lift. The areas of cross section of the press piston and pump piston are 72 m² and 0.6 m², respectively. Arrange the following steps in a proper order to find the effort applied on the pump piston and mechanical advantage of hydraulic lift by using load and effort.
(A) Pressure is equal on both the press and pump pistons, i.e., P₁ = P₂ or $\frac{F_1}{a_1}=\frac{F_2}{a_2}$
(B) Find the mass of the trolley, areas of cross section of pump piston and press piston from the given data.
(C) The force on the press piston (F₂) is equal to weight of the trolley, this is the load.
(D) The amount of force (F₁) needed to be applied on the pump piston to lift the trolley is effort.
(E) The mechanical advantage of the hydraulic machine is the ratio of load to effort.

• A. ABCDE
• B. ADCBA
• C. BCDAE
• D. BCAED

Answer 1

The correct option is C

BCDAE

1. Mass of the trolley and area of cross section of pump piston and press piston are found taken from the given data .---(B)
2. Force on the pump piston is denoted as ${\mathrm{F}}_2\mathrm{and}\mathrm{that}\mathrm{on}\mathrm{the}\mathrm{press}\mathrm{piston}\mathrm{is}{\mathrm{F}}_1\mathrm{now}\mathrm{the}{\mathrm{F}}_2=\mathrm{weight}\mathrm{of}\mathrm{the}\mathrm{trollery}\mathrm{which}\mathrm{is}\mathrm{the}\mathrm{load}.$--(C)
3. we know that effort is the force ($F_1$) required to lift a weight on the trolley----(D)
4. According to pascal's law the pressure on both pistons are equal$\Rightarrow \frac{{\mathrm{F}}_1}{{\mathrm{a}}_1}=\frac{{\mathrm{F}}_2}{{\mathrm{a}}_2}\mathrm{or}{\mathrm{P}}_1={\mathrm{P}}_2$----(A)
5. Now load and effort are found out which when put in the formula will give the mechanical advantage ----(E)
   $\frac{\mathrm{load}}{\mathrm{effort}}=\mathrm{Mechanical}\mathrm{advantage}$
   hence BCDAE