Write short notes on the following.
(a) Unit

Derive the equations of motion for a particle
(a) falling vertically
(b) projected vertically.

Consider a circular road of radius 20 meter banked at an angle of 15 degree. With what speed a car has to move on the turn so that it will have safe turn?

Explain the method to find the center of gravity of a irregularly shaped lamina?

A fly wheel rotates with a uniform angular acceleration. If its angular velocity increases from 20\(\pi\) rad/s to 40\(\pi\) rad/s in 10 seconds. Find the number of rotations in that period.

Derive an expression for escape speed.

Derive an expression for the elastic energy stored per unit volume of a wire.

Explain in detail an adiabatic process.

Discuss the simple pendulum in detail.

Write short notes on intensity and loudness.