What Is The Significance Of Entropy?

As per the second law of thermodynamics, any heat input to the system (Heat engine) cannot be converted completely into useful work. Some energy is lost and that is called 'unavailable work'. The amount of unavailable work increases as the entropy increases. So we can conclude that entropy is the measure of work of the system.

Will a bullet fired from a gun perpendicular to the earth's surface return to the earth?

If you fired the bullet greater than the escape velocity (more accurately greater the escape-velocity/√2), the bullet will not return in the earth. For earth, the value of escape velocity is 11.2 km/sec. Because at a higher velocity, the bullet will get a huge kinetic energy and so that the bullet will easily overcome gravitational force of the earth. Note: Normally a bullet can not achieve this high velocity. So, it will hit on the ground.

Why cavitation will occur in Centrifugal Pumps and not in Displacement pumps?

The formation of cavities (or bubbles) is induced by flow separation, or non-uniform flow velocities, inside a pump casing. In centrifugal pumps the eye of the pump impeller is smaller than the flow area of pipe. This decrease in flow area of pump results in increase in flow rate. So pressure drop happened between pump suction and the vanes of the impeller. Here air bubbles or cavities are formed because of liquid vapour due to increase in temperature in impeller. This air bubbles are transmitted to pump which forms cavitation.