A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inversely proportional to R³. Its time period of revolution will be given by :

A clock has a continuously moving second's hand of 0.1 m length. The average acceleration of the tip of the hand (in units of ms^–2) is of the order of :

A bead of mass m stays at point P(a, b) on a wire bent in the shape of a parabola y = 4Cx² and rotating with angular speed $$\omega $$ (see figure). The value of $$\omega $$ is (neglect friction) :

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 :