A uniform disc of mass `0.5kg` and radius `r` is projected with velocity `18m/s` at `t=0s` on a rough horizontal surface.It starts off with a purely sliding motion at `t=0`.After `2s` it acquires a purely rolling motion (see figure).The total kinetic energy of the disc after `2s` will be `g=10m/s^(2)`

A uniform disc of mass m and radius R is projected horizontally with velocity v_(0) on a rough horizontal floor so that it starts off with a purely sliding motion at t=0 . After t_(0) seconds, it acquires pure rolling motion as shown in the figure. (a) Calculate the velocity of the center of mass of the disc at t_(0) . Assuming that the coefficent of friction to be mu , calculate t_(0) .

A uniform disc of mass m and radius R is projected horizontally with velocity v_(0) on a rough horizontal floor so that it starts with a purely sliding motion at t= 0. After t_(0) seconds it acquires a purely rolling motion. (a) Calculate the velocity of the centre of mass of the disc at t_(0) (b) Assuming the coefficient of friction to be mu , calculate to. Also calculate the work done by the frictional force as a function of time and the total work done by it over a time t muchlonger than t_(0) .

A uniform ring of mass 'm' and radius 'R' is projected horizontally with velcoty v_(0) on a rough horizontal floor, so that it starts off with a purely sliding motion and it acquires a pure rolling motion after moving a distance d. If the coefficient of friction between the ground and ring is mu , then work done by the friction in the process is

A block is kept on a rough horizontal surface. A variable horizontal force is acting on the block as shown in the figure. At t=0 , block is at rest. Kinectic energy of block at t=5 sec will be (g=10m//s^(2))

A particle is projected with velocity of 10m/s at an angle of 15° with horizontal.The horizontal range will be (g = 10m/s^2)

A circular disc of mass 0.41 kg and radius 10 m rolls without slipping with a velocity of 2 m/s. The total kinetic energy of disc is

A solid cylinder of mass 1 kg and radius 0.02 m, is rolling on a smooth horizontal surface with a uniform velocity of 0.1 m/s. Its total energy is