A particle is moving with uniform speed along the circumference of a circle of radius $R$ under the action of a central fictitious force $F$ which is inversely proportional to $R ^{3}$. Its time period of revolution will be given by
$T \propto R ^{2}$
$T \propto R ^{\frac{3}{2}}$
$T \propto R ^{\frac{5}{2}}$
$T \propto R ^{\frac{4}{3}}$
A particle is revolving in a circular path of radius $25 \,m$ with constant angular speed $12 \,rev/min$. Then the angular acceleration of particle is .......... $rad / s ^2$
An athlete completes one round of a circular track of radius $10\, m$ in $40\, sec$. The distance covered by him in $2 \,min$ $20 \,sec$ is ........ $m$
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 is moving with a constant speed $v$ in a circle. What is the magnitude of average velocity after half rotation
A particle, moving with uniform speed $v$, changes its direction by angle $\theta$ in time $t$. Magnitude of its average acceleration during this time is