A particle revolves round a circular path. The acceleration of the particle is

A particle moves with constant angular velocity in circular path of certain radius and is acted upon by a certain centripetal force $F$. if the centripetal force $F$ is kept constant but the angular velocity is doubled, the new radius of the path (original radius $R$ ) will be

The acceleration vector of a particle in uniform circular motion averaged over the cycle is a null vector. This statement is

A particle moves so that its position vector is given by $\overrightarrow {\;r} = cos\omega t\,\hat x + sin\omega t\,\hat y$ , where $\omega$ is a constant.  Which of the following is true?  

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,:

The length of second's hand in a watch is $1 \,cm.$ The change in velocity of its tip in $15\, seconds$ is