Question

In a hydraulic lift, used at a service station the radius of the large and small piston are in the ratio of 20 : 1. what weight placed on the small piston will be sufficient to lift a car of mass 1500 kg ?

A.3.75kg
B.37.5kg
C.7.5kg
D.75kg

Answer 1

Using Pascal's Principle and the given ratio of the piston radii, the weight needed to be placed on the small piston to lift a 1500 kg car is calculated to be 37.5 kg. Therefore, the correct option is B.

Step-by-step explanation:

To determine the weight placed on the small piston to lift a car of mass 1500 kg using a hydraulic lift, we can use Pascal's Principle which states that pressure is transmitted undiminished in an enclosed fluid. Thus, the relationship between the force applied on the small piston (F1), its area (A1), and the force necessary to lift the car (F2), and its area (A2) is given by:

F1/A1 = F2/A2

The areas are related to the radii of the pistons (r1 and r2), where A1 = π * r12 and A2 = π * r22. Given the radii are in the ratio of 20:1, this means their areas are in a ratio of 400:1, since area is proportional to the square of the radius.

For a car of mass 1500 kg, the weight (F2) is the mass multiplied by the acceleration due to gravity (9.81 m/s2), so F2 = 1500 kg * 9.81 m/s2.

We can then solve for F1 using the ratios:

F1 = F2 / 400

After calculating, we find that the weight that needs to be placed on the small piston is 37.5 kg.

Therefore, the correct answer is:

B.37.5kg