A ball of mass $0.5 \mathrm{~kg}$ is attached to a string of length $50 \mathrm{~cm}$. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is $400 \mathrm{~N}$. The maximum possible value of angular velocity of the ball in rad/s is,:

A car is going round a circle of radius $R_1$ with constant speed. Another car is going round a circle of radius $R_2$ with constant speed. If both of them take same time to complete the circles, the ratio of their angular speeds and linear speeds will be .........

A particle $P$ is moving in a circle of radius $'a'$ with a uniform speed $v$ . $C$ is the centre of the circle and $AB$ is a diameter. When passing through $B$ the angular velocity of $P$ about $A$ and $C$ are in the ratio 

The angular velocity of a wheel is $70\, rad/sec$. If the radius of the wheel is $0.5\, m$, then linear velocity of the wheel is ....... $m/sec$

Two particles each of mass $m$ are moving in horizontal circle with same angular speed. If both string are of same length then the ratio of tension in string $\frac{T_1}{T_2}$ is .........

The linear speed of the tip of seconds hand of a wall clock is $1.05\,cm\,s^{-1}.$ The length of the seconds hand is nearly  ........ $cm$