Class 12 Maharashtra State Board

In a hydraulic lift, the input piston had surface area 30 cm² and the output piston has surface area of 1500 cm² . If a force of 25 N is applied to the input piston, calculate weight on output piston.

As per the given question we can list some given data as

$https://latex.codecogs.com/svg.image?Input Area A_{1}= 30 cm^{2}= 30 \mathrm{x}10^{-4}m^{2}$

$https://latex.codecogs.com/svg.image?Output Area A_{2}= 1500 cm^{2}= 1500 \mathrm{x}10^{-4}m^{2}$

Input force F₁ = 25N

To find, weight at the output piston F₂ = ?

Solution -

Using Pascals Law we can write ,

Input Pressure = Output Pressure

$https://latex.codecogs.com/svg.image? \frac{F_{1}}{A_{1}}=\frac{F_{2}}{A_{2}}$

$https://latex.codecogs.com/svg.image?F_{2}=\frac{F_{1}A_{2}}{A_{1}}$

$https://latex.codecogs.com/svg.image?F_{2}=\frac{25 \mathrm{x 1500 \mathrm{x}10^{-4}}}{30 \mathrm{x 10^{-4}}}$

F₂ = 25 x 50 = 1250 N

The mass of the earth is 6 x 10²⁴ kg. The distance between the earth and the Sun is 1.5x 10¹¹ m. If the gravitational force between the two is 3.5 x 10²² N, what is the mass of the Sun?