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

Two racing cars of masses ${m_1}$ and ${m_2}$ are moving in circles of radii ${r_1}$ and ${r_2}$ respectively. Their speeds are such that each makes a complete circle in the same duration of time $t$. The ratio of the angular speed of the first to the second car is

The second's hand of a watch has length $6\,\, cm$. Speed of end point and magnitude of difference of velocities at two perpendicular positions will be

Two particles $A$ and $B$ start at the origin $O$ and travel in opposite directions along the circular path at constant speeds $0.5\,m/s$ and $1.5\,m/s$ , respectively. The time when they collide with each other ........ $\sec$

The driver of a car travelling at velocity $v$ suddenly see a broad wall in front of him at a distance $d$. He should

A ball of mass $0.1$ kg is suspended by a string. It is displaced through an angle of ${60^o}$ and left. When the ball passes through the mean position, the tension in the string is ........ $N$