A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance $'r'$. The speed of the particle is

A vehicle is moving with a velocity $v$  on a curved road of width $b$  and radius of curvature $R.$  For counteracting the centrifugal force on the vehicle, the difference in elevation required in between the outer and inner edges of the road is

A train is running at $20 \,m / s$ on a railway line with radius of curvature $40,000$ metres. The distance between the two rails is $1.5$ metres. For safe running of train the elevation of outer rail over the inner rail is ......$mm$ $\left( g =10 \,m / s ^2\right)$

A stone of mass of $16\, kg$ is attached to a string $144 \,m$ long and is whirled in a horizontal circle. The maximum tension the string can withstand is $16$ Newton. The maximum velocity of revolution that can be given to the stone without breaking it, will be ....... $ms^{-1}$

Write the formula for the maximum permissible speed of a vehicle moving on smooth circular balanced tracks.

A car of mass $800 \,kg$ moves on a circular track of radius $40\, m$. If the coefficient of friction is $0.5$, then maximum velocity with which the car can move is ......... $m/s$