The outer rail of a curved railway track is generally raised over the inner. Why?

Two cars having masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. If they go once round their circles in equal time, find the ratio of their angular speeds.

Define centripetal force and establish an expression for the same.

Explain what you understand by centripetal and centrifugal forces. Establish an expression for centripetal force.

What is meant by banking of roads? Why is it necessary? Deduce an expression for the angle of banking and hence show that a road of definite radius can be ideally banked for a particular value of highest speed. 

Why centripetal forces are real forces and centrifugal force is called a pseudo force?

An automobile of mass $1200 \mathrm{kg}$ has to make a circular turn of radius $40 \mathrm{m}$. If it is moving with a speed of $10 \mathrm{m}/\mathrm{s}$, what is the centripetal force on the automobile?