You may have seen in a circus a motorcyclist driving in vertical loops inside a ‘death- well’ (a hollow spherical chamber with holes, so the spectators can watch from outside). Explain clearly why the motorcyclist does not drop down when he is at the uppermost point, with no support from below. What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is 25 m ?

Dimensionally prove the expression (mv^(2))/( r) for the centripetal force F acting on a particle of mass m moving with velocity v in a circle of radius r.

Prove that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed is 6sqrt3r .

A particle of mass m moves with speed v_0 in a circle of radius r_0 on a frictionless table-top. The particle is attached to a string that passes through a hole in the table as shown in figure. The string is slowly pulled downward so that the particle moves in a smaller circle of radius r_f .find the tension when the particle is moving in a circle of radius r_f in terms of m, r and the angular momentum L_0 = mv_0r_0

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is (2R)/(sqrt(3)) . Also find the maximum volume.

A small particle of mass m attached with a light inextensible thread of length L is moving in a vertical circle. In the given case the particle is moving in a complete vertical circle and ration of its maximum to minimum velocity is 2 : 1. Velocity of the particle when it is moving vertically downward is

A small particle of mass m attached with a light inextensible thread of length L is moving in a vertical circle. In the given case the particle is moving in a complete vertical circle and ration of its maximum to minimum velocity is 2 : 1. The kinetic energy of the particle at the lowest position is