A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length $$\ell $$. The other end is fixed. The system is given an angular speed $$\omega $$ about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is :

A smooth wire of length 2$$\pi $$r is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed $$\omega $$ about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then the value of $$\omega $$² is equal to -

A particle is moving along a circular path with a constant speed of 10 ms^–1. What is the magnitude of the change in velocity of the particle, when it moves through an angle of 60^o around the centre of the circle?

A body is projected at t = 0 with a velocity 10 ms^–1 at an angle of 60^o with the horizontal. The radius of curvature of its trajectory at t = 1s is R. neglecting air resistance and taking acceleration due to gravity g = 10 ms^–2, the value of R is :