Uniform Circular Motion — Prelims Questions

A particle is moving in a circle of radius $R$ with constant speed $v$. The magnitude of its average acceleration over a time interval during which it completes half a revolution is:

A stone of mass $m$ is tied to a string of length $L$ and whirled in a horizontal circle with a constant speed $v$. The tension in the string is $T$. Which of the following statements is correct?

An object of mass $5,\text{kg}$ is moving in a circle of radius $2,\text{m}$ with an angular velocity of $3,\text{rad/s}$. Calculate the centripetal force acting on the object.

A car is negotiating a curved road of radius $R$. The road is banked at an angle $heta$. The coefficient of static friction between the tires and the road is $mu_s$. What is the maximum safe speed for the car to negotiate the curve without skidding?

Two particles of masses $m_1$ and $m_2$ are moving in concentric circles of radii $r_1$ and $r_2$ respectively. If their periods of revolution are the same, what is the ratio of their linear speeds ($v_1/v_2$)?

A body moves in a circular path with decreasing speed. Which of the following statements is true regarding its acceleration?