$A$ body of mass $m$ attached at the end of a string is just completing the loop in a vertical circle. The apparent weight of the body at the lowest point in its path is ($g =$ gravitational acceleration).

$A$ body of mass $m \ kg$ slides from rest along the curve of a vertical circle from point $A$ to $B$ on a frictionless path. The velocity of the body at $B$ is: (Given: $R = 14 \ m$,$g = 10 \ m/s^2$,and $\sqrt{2} = 1.4$) (in $m/s$)

$A$ small cube with mass $M$ starts at rest at point $1$ at a height $4R$,where $R$ is the radius of the circular part of the track. The cube slides down the frictionless track and around the loop. The force that the track exerts on the cube at point $2$ is nearly ......... times the cube's weight $mg$.

$A$ sphere is suspended by a thread of length $l$. What minimum horizontal velocity has to be imparted to the ball for it to reach the height of the suspension point?

In the given figure,for an initial velocity $u = u_0/3$,find the height from the ground at which the block leaves the hemisphere,where $u_0 = \sqrt{gr}$.

$A$ particle is moving along a vertical circle of radius $R$. At point $P$,what will be the velocity of the particle? (Assume the critical condition at the highest point $C$).