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 a force of constant magnitude acts in direction perpendicular to the motion of a particle, then its

Two particles $A$ and $B$ are moving in uniform circular motion in concentric cirdes of radius $r_{A}$ and $r_{B}$ with speed $v_A$ and $v_B$ respectively. The time period of rotation is the same. The ratio of angular speed of $A$ to that of $B$ will be

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

Four particles $A, B, C$ and $D$ are moving with constant speed $v$ each. At the instant shown relative velocity of $A$ with respect to $B, C$ and $D$ are in directions

A cyclist starts from centre 0 of a circular park of radius $1\, km$ and, moves along the path $OPRQO$ as shown in figure.

If he maintains constant speed of $10\, ms^{-1}$, what is his acceleration at point $R$ in magnitude and direction ?