Radius of gyration of a thin uniform rod of length ' $L$ ' about an axis passing through its centre and perpendicular to its length is

A thin circular ring and a circular disc of equal mass are rolling without sliding. If their linear velocities are equal and the total kinetic energy of the disc is 6 J , then the total kinetic energy of the ring is

A body of mass 4 kg attached to a spring of force constant $64 \mathrm{Nm}^{-1}$ executes simple harmonic motion on a frictionless horizontal surface. The time period of oscillation is

A particle is executing simple harmonic motion with amplitude $A$. At a distance ' $x$ ' from the mean position, when the particle is moving towards extreme position it receives a blow in the direction of motion which instantaneously doubles its velocity. The new amplitude of the particle is

(Frequency is constant during the motion)