A ring and a disc roll on the horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is 4 J then total kinetic energy of the disc is

Step-by-step solution

Total K.E of the rolling disc or ring is given by. K . E = 1 2 m v 2 + 1 2 I ω 2 For ring and disk, translational kinetic energy 1 2 m v 2 is constant. Rolling K.E. of disc is 1 4 m R 2 ω 2 Rolling K.E. of ring is 1 2 m R 2 ω 2 As for ring, 4 J = 1 2 m v 2 + 1 2 m R 2 ω 2 ∴ m R 2 ω 2 = 4 J For disc 1 2 m R 2 ω 2 + 1 4 m R 2 ω 2 = 4 2 + 4 4 J = 2 + 1 J = 3 J