Two cars $S_1$ and $S_2$ are moving in coplanar concentric circular tracks in the opposite sense with the periods of revolution $3 \,min$ and $24 \,min$, respectively. At time $t=0$, the cars are farthest apart. Then, the two cars will be 

A ring of mass $m$ moves from point $1$ to point $2$ along a smooth rigid horizontal wire with a constant speed $v$. The average force acting the ring over the time of its motion from $1$ to $2$ is

An athlete completes one round of a circular track of radius $10\, m$ in $40\, sec$. The distance covered by him in $2 \,min$ $20 \,sec$ is ........ $m$

A particle is tied to $20\, cm$ long string. It performs circular motion in vertical plane. What is the angular speed of particle when the tension in the string at the top is  zero   ......... $rad/sec$

If the string of a conical pendulum makes an angle $\theta$ with horizontal, then square of its time period is proportional to

A particle moving with uniform speed in a circular path maintains: