Dynamics of Uniform Circular Motion — Prelims Questions

A particle of mass $m$ is moving in a horizontal circle of radius $r$ with a constant speed $v$. What is the magnitude of the net force acting on the particle?

A car is moving on a circular track of radius $50\,\text{m}$ at a speed of $10\,\text{m/s}$. If the mass of the car is $1000\,\text{kg}$, what is the minimum coefficient of static friction required between the tires and the road to prevent skidding?

A $2\,\text{kg}$ mass is attached to a string and whirled in a vertical circle of radius $1\,\text{m}$. If the speed of the mass at the lowest point is $5\,\text{m/s}$, what is the tension in the string at that point? (Take $g = 10\,\text{m/s}^2$)

An object moves in a circular path with constant speed. Which of the following statements is TRUE?

A conical pendulum consists of a mass $m$ attached to a string of length $L$. The mass revolves in a horizontal circle with constant speed $v$, and the string makes an angle $\theta$ with the vertical. Which of the following expressions correctly relates $v$, $L$, $\theta$, and $g$?

A road is banked at an angle $\theta$ for a vehicle moving at an ideal speed $v$. If the radius of curvature of the road is $R$, which of the following expressions is correct for the ideal speed?