An annular disc has a mass m, inner radius R and outer radius $$2R$$. The disc rolls on a flat surface without slipping. If the velocity of the center of mass is $$v,$$ the kinetic energy of the disc is

A four-wheel vehicle of mass 1000kg moves uniformly in a straight line with the wheels revolving at 10 rad/s. The wheel are identical, each with a radius of 0.2 m. Then a constant braking torque is applied to all the wheels and the vehicle experiences a uniform deceleration. For the vehicle to stop in 10s, the braking torque (in N. m) on each wheel is ___________.

A body of mass (m) 10kg is initially stationary on a 45° inclined plane as shown in figure. The coefficient of dynamic friction between the body and the plane is 0.5. The body slides down the plane and attains a velocity of 20 m/s. The distance travelled (in meter) by the body along the plane is _______

A pin jointed uniform rigid rod of weight W and length is supported horizontally by an external force F as shown in the figure below. The force F is suddenly removed. At the instant of force removal, the magnitude of vertical reaction developed at the support is