A stone tide to a spring of length L is whirled in a vertical circle with the other end of the spring at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is $$\sqrt {x({u^2} - gL)} $$. The value of x is -

A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point Q is A while angular position of point Q is $$\alpha$$ with respect to point P. Which of the following graphs represent the correct relation between A and $$\alpha$$ when ball goes from Q to R?

A disc with a flat small bottom beaker placed on it at a distance R from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $$\omega$$. The coefficient of static friction between the bottom of the beaker and the surface of the disc is $$\mu$$. The beaker will revolve with the disc if :

For a particle in uniform circular motion, the acceleration $$\overrightarrow a $$ at any point P(R, $$\theta$$) on the circular path of radius R is (when $$\theta$$ is measured from the positive x-axis and v is uniform speed) :