Two 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 they make complete circles in the same time $t$. The ratio of their centripetal acceleration is

A ring of mass $m$ moves from point $1$ to point $2$ along a smooth rigid horizontal wire with a constant speed $v$. The average force acting the ring over the time of its motion from $1$ to $2$ is

A particle moves in $x-y$ plane according to rule $x = {\rm{asin}}\omega t$ and $\;y = {\rm{acos}}\omega t$. The particle follows  

A particle describes a horizontal circle of radius $r$ on the smooth surface of an inverted cone as shown. The height of plane of circle above vertex is $h$. The speed of particle should be

$Assertion$ : When a particle moves in a circle with a uniform speed, its velocity and acceleration both changes.

$Reason$ : The centripetal acceleration in circular motion is dependent on angular velocity of the body.

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 ........ $m$