A ball is moving uniformly in a circular path of radius $1 m$ with a time period of $1.5 \,s$. If the ball is suddenly stopped at $t=8.3 \,s$, the magnitude of the displacement of the ball with respect to its position at $t=0 \,s$ is closest to .......... $m$

A particle comes round a circle of radius $1 \,m$ once. The time taken by it is $10 \,sec$. The average velocity of motion is

Two racing cars of masses ${m_1}$ and ${m_2}$ are moving in circles of radii ${r_1}$ and ${r_2}$ respectively. Their speeds are such that each makes a complete circle in the same duration of time $t$. The ratio of the angular speed of the first to the second car is

The kinetic energy $k$ of a particle moving along a circle of radius $R$ depends on the distance covered $s$ as $k = as^2$ where $a$ is a constant. The force acting on the particle is

A particle is revolving in a circle of radius $2\ m$ with angular velocity $\omega = t^2 -4t + 8\ rad/s$ . The time when speed of the particle becomes $8\ m/s$ is    ......... $\sec$

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