$A$ car moving at a speed of $72 \; km/hr$ passes through a point $P$ on a curved road with a radius of $10 \; m$. The mass of the car is $500 \; kg$. Find the contact force (normal force) at point $P$ in $kN$. (Take $g = 10 \; m/s^2$)

$A$ particle of mass $m$ is rotating in a plane in a circular path of radius $r$. Its angular momentum is $L$. The centripetal force acting on the particle is

$A$ coin placed on a rotating turntable just slips if it is placed at a distance of $4 \ cm$ from the centre. If the angular velocity of the turntable is doubled,it will just slip at a distance of: (in $cm$)

$A$ roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is $20\, m$. The speed of the car at the top of the hill is between

If the radii of circular paths of two particles of same mass are in the ratio of $1: 2$,then to have a constant centripetal force,the ratio of their speeds should be

$A$ dumbbell is placed on a frictionless horizontal table. Sphere $A$ is attached to a frictionless pivot so that $B$ can be made to rotate about $A$ with constant angular velocity. If $B$ (mass $2M$) makes one revolution in period $P$,the tension in the rod (length $d$) is