Pascal's Law — Prelims Questions

A hydraulic lift is designed to lift cars. The area of the input piston is $0.05\,\text{m}^2$ and the area of the output piston is $2.5\,\text{m}^2$. If a car weighing $15000\,\text{N}$ is to be lifted, what minimum force must be applied to the input piston?

Which of the following conditions is NOT essential for Pascal's Law to be accurately applied?

In a hydraulic press, the diameter of the small piston is $10\,\text{cm}$ and the diameter of the large piston is $50\,\text{cm}$. If a force of $200\,\text{N}$ is applied to the small piston, what is the maximum force that can be lifted by the large piston?

A hydraulic press has an input piston of radius $r$ and an output piston of radius $3r$. If the input piston is pushed down by a distance $x$, by what distance will the output piston rise?

A hydraulic system has two pistons. The smaller piston has a cross-sectional area of $5\,\text{cm}^2$ and the larger piston has a cross-sectional area of $100\,\text{cm}^2$. If the smaller piston is subjected to a pressure of $200\,\text{kPa}$, what is the force exerted on the larger piston?

A student observes that when he presses a sealed plastic bottle filled with water, the water level in a thin tube inserted into the bottle rises. This phenomenon best illustrates:

A hydraulic brake system in a car uses a master cylinder with a piston of area $2\,\text{cm}^2$ and wheel cylinders with pistons of area $10\,\text{cm}^2$. If the driver applies a force of $50\,\text{N}$ on the brake pedal, and the pedal mechanism multiplies this force by a factor of 4 before it reaches the master cylinder, what is the total braking force exerted by one wheel cylinder?