A body of mass '$$\mathrm{m}$$' 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 ( $$\mathrm{g}$$ = gravitational acceleration)

A railway track is banked for a speed ',$$v$$' by elevating outer rail by a height '$$h$$' above the inner rail. The distance between two rails is 'd' then the radius of curvature of track is ( $$\mathrm{g}=$$ gravitational acceleration)

Two particles having mass '$$M$$' and '$$m$$' are moving in a circular path with radius '$$R$$' and '$$r$$' respectively. The time period for both the particles is same. The ratio of angular velocity of the first particle to the second particle will be

In a conical pendulum the bob of mass '$$\mathrm{m}$$' moves in a horizontal circle of radius '$$r$$' with uniform speed '$$\mathrm{V}$$'. The string of length '$$\mathrm{L}$$' describes a cone of semi vertical angle '$$\theta$$'. The centripetal force acting on the bob is ( $$\mathrm{g}=$$ acceleration due to gravity)