A cylindrical vessel partially filled with water is rotated about its vertical central axis. It’s surface will

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 ........ $\sec$

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

A conical pendulum of length $1\,m$ makes an angle $\theta \, = 45^o$ w.r.t. $Z-$ axis and moves in a circle in the $XY$ plane.The radius of the circle is $0.4\, m$ and its centre is vertically below $O$. The speed of the pendulum, in its circular path, will be ..... $m/s$ (Take $g\, = 10\, ms^{-2}$)

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

Two particles having mass $M$ and $m$ are moving in a circular path having radius $R$ and $r$. If their time period are same then the ratio of angular velocity will be