If speed of a particle moving in a circle of radius $2\,m$ is given as $v = 2t + 2$, then its centripetal acceleration after $1\, s$ will be   ......... $m/s^2$

The net applied force on a body in uniform circular motion should always be

A proton of mass $ 1.6  \times 10^{-27} kg$ goes round in a circular orbit of radius $0.10\, m$ under a centripetal force of $4  \times 10^{-13}\, N$. then the frequency of revolution of the proton is about 

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

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 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