For a hydraulic lift with dimensions shown in figure, assuming g = 10 m/s 2 , the maximum diameter Dleft (in m) that lifts a vehicle of mass 1000 kg using a force

Q. For a hydraulic lift with dimensions shown in figure, assuming g = 10 m/s ² , the maximum diameter D_left (in m) that lifts a vehicle of mass 1000 kg using a force of 100 N is__________________(rounded off to two decimal places).

Solution:

Using pascals principle, pressure on both sides must be equal 

pressure = force / area

Force_left = 100N

Area_left = pi/4 * d_left * d_left

Force_right = mass * gravity = 1000 * 10 = 10000N

Area_left = pi/4 * d_right * d_right = pi/4 * 2 *2 

Equating pressure on both sides

pressure_left =pressure_right

force_left/area_left = force_right/area_right

100/(pi/4 * d_left *d_left) = 10000/(pi/4 * 2 *2)

1/(d_left * d_left) = 100/ (2*2)

Which solves to 

D_left = 0.2 m