A car is moving on a horizontal circular track of radius $0.2 \,km$ with a constant speed. If coefficient of friction between tyres of car and road is $0.45$, then speed of car may be ........ $m / s$ [Take $g=10 \,m / s ^2$ ]

A particle moves in a horizontal circle on the smooth inner surface of a hemispherical bowl of radius $R$. The plane of motion is at a depth $d$ below the centre of the hemisphere. The speed of the particle is :-

A particle is moving in a circle of radius $R$ with constant speed $v$, if radius is double then its centripetal force to keep the same speed should be

An annular ring with inner and outer radii $R_{1}$ and $R_{2}$ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, $\frac{F_{1}}{F_{2}}$ is

On a railway curve, the outside rail is laid higher than the inside one so that resultant force exerted on the wheels of the rail car by the tops of the rails will

$A$ particle is moving in a circle :