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 doubled, keeping radius the same, the new force will be

The second's hand of a watch has length $6\,\, cm$. Speed of end point and magnitude of difference of velocities at two perpendicular positions will be

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

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

A sphere of mass $m$ is tied to end of a string of length $l$ and rotated through the other end along a horizontal circular path with speed $v$. The work done in full horizontal circle is

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