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?

A body of mass $2 \mathrm{g}$ is set to rotate in a circular path by means of a string $100 \mathrm{cm}$ long. If it makes $3$ complete revolutions in $1.2 \mathrm{s}$, find the tension of the string.

A particle moves in a circle of radius $0.5 \mathrm{m}$. Its linear speed is given by $v=3t$ where $t$ is in second and $v$ in $\mathrm{m} {\mathrm{s}}^{-1}$. Find the radial and tangential acceleration at $t=5 \mathrm{s}$.

A cyclist, running at $18 \mathrm{km} {\mathrm{h}}^{-1}$ speed, took a turn along a curved path of radius $20 \mathrm{m}$. What was his inclination with the vertical plane? $g=980 \mathrm{cm} {\mathrm{s}}^{-2}$.

The curvature of a railway line has radius $45 \mathrm{m}$ and the distance between the two lines is $1.5 \mathrm{m}$. If the outer line is $12.5 \mathrm{cm}$ higher than the inner, at what maximum speed can an engine bend round the curve without exerting lateral pressure on the lines?

A roadway bridge over a river is in the form of a quarter of a circle of radius $60 \mathrm{m}$. What is the maximum speed with which a car must pass over the bridge without leaving the ground at any point of it? ($g=9.8 \mathrm{m}/{\mathrm{s}}^2$)

A cyclist, going $5 \mathrm{m}/\mathrm{s}$ speed, turns round a bend of radius $2 \mathrm{m}$. If the mass of the cyclist be $50 \mathrm{kg}$, what will be the centrifugal force acting on the cyclist? How many time is it more than his own weight?

A particle of mass $10 \mathrm{g}$ is moving in a circle of radius $0.5 \mathrm{m}$ with an angular velocity of $6 \mathrm{rad}/\mathrm{s}$. Find the change in linear velocity in half a revolution.