$A$ particle moves in a circular path inside a cone with speed $v$. Then:

$A$ mass of $100\, g$ is tied to one end of a string $2\, m$ long. The body is revolving in a horizontal circle making a maximum of $200$ revolutions per minute. The other end of the string is fixed at the center of the circle of revolution. The maximum tension that the string can bear is .......... $N$ (approximately).

$A$ car is moving with velocity $v$ at the top of a semi-circular hill of radius $40 \,m$ such that the normal force on it is zero. Find the velocity $(v)$ of the car. [Use $g=10 \,ms^{-2}$] (in $\,ms^{-1}$)

$A$ uniform chain of mass $m$ and length $L$ is originally placed mid-way on the top of a fixed smooth double-sided wedge. The length of each side of the wedge is $L$. It is then given a slight push. The kinetic energy of the chain when the whole chain has just slid to the left side of the wedge is:

$A$ car of mass $m$ is crossing a convex bridge of radius of curvature $R$ with speed $V$. At the highest point, the thrust (normal force) is ($g =$ gravitational acceleration).

When a vehicle of mass $m$ is moving with a velocity $v$ over a concave over-bridge of radius of curvature $r$,the thrust on the road at the lowest point on the bridge will be