Circular Motion — Prelims Questions

A particle is moving in a horizontal circle of radius $R$ with a constant speed $v$. If the radius is doubled to $2R$ and the speed is also doubled to $2v$, what is the ratio of the new centripetal force to the original centripetal force?

A car is moving on a circular track of radius $100,\text{m}$ with a speed of $20,\text{m/s}$. If the coefficient of static friction between the tires and the road is $0.4$, will the car skid? (Take $g = 10,\text{m/s}^2$)

A particle of mass $m$ is moving in a vertical circle of radius $r$. What is the difference in tension in the string at the lowest point and the highest point of the circle, if its speed at the lowest point is $v_L$ and at the highest point is $v_H$?

A particle moves in a circle of radius $5,\text{m}$ with a constant angular acceleration of $2,\text{rad/s}^2$. If the particle starts from rest, what is its total acceleration after $2,\text{s}$?

A body of mass $M$ is moving in a circular path of radius $R$ with a constant speed $v$. The work done by the centripetal force in half a revolution is:

A cyclist is riding at a speed of $18,\text{km/h}$ on a level circular road of radius $30,\text{m}$. What is the angle of inclination with the vertical if he is to safely negotiate the turn without skidding? (Take $g = 10,\text{m/s}^2$)

A stone of mass $0.2,\text{kg}$ is tied to one end of a string $0.8,\text{m}$ long and whirled in a horizontal circle at a constant speed. If the string can withstand a maximum tension of $20,\text{N}$, what is the maximum speed with which the stone can be whirled?