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 angular velocity is kept same but the radius of the path is halved, the new force will be

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   ......... $m/s^2$

Two spheres $P$ and $Q$ of equal masses are attached to a string of length $2\,\, m$ as shown in figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant rate. What is the value of the ratio
$\left( {\frac{{{\text{Tension in the string between P and Q}}}}{{{\text{Tension in the string between P and O}}}}} \right)?$

A car goes around uniform circular track of radius $R$ at a uniform speed $v$ once in every $T$ seconds. The magnitude of the centripetal acceleration is $a_c$. If the car now goes uniformly around a larger circular track of radius $2 R$ and experiences a centripetal acceleration of magnitude $8 a_c$. Then, its time period 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  ........ $cm$

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