A stone of mass $1\,kg$ is tied to end of a massless string of length $1\,m$. If the breaking tension of the string is $400\,N$, then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is $.......\,ms^{-1}$

A ball of mass $( m )=0.5 \ kg$ is attached to the end of a string having length $(L)$ $=0.5 m$. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is $324 \ N$. The maximum possible value of angular velocity of ball (in radian/s) is

If the length of the second's hand in a stop clock is $3 \,cm$ the angular velocity and linear velocity of the tip is

A car is moving with speed $30$ $m/\sec $ on a circular path of radius $500\, m$. Its speed is increasing at the rate of $2m/{\sec ^2},$ What is the acceleration of the car ........ $m/sec^2$

An object moves at a constant speed along a circular path in horizontal $XY$ plane with centre at origin. When the object is at  $x = -2\,m$ , its velocity is $-(4\,m/ s)\hat j$ . What is object's acceleration when it is at $y = 2\,m$ ?

A particle moves in $x-y$ plane according to rule $x = {\rm{asin}}\omega t$ and $\;y = {\rm{acos}}\omega t$. The particle follows