A disc of mass 5 kg and radius 50 cm rolls on the ground at the rate of 10 ~ms ⁻¹ . Find the kinetic energy of the disc in J .

Step-by-step solution

Here, mass of the disc, M=5 ~kg Radius of the disc, R=50 ~cm =1 / 2 ~m Linear velocity of the disc, v=10 ~ms ⁻¹ As, v=R 10= 1 2 or =10 2=20 rad s ⁻¹ Also, moment of inertia of disc about an axis through its centre, I= 1 2 M R^2= 1 2 5 ( 1 2 )^2= 5 8 ~kg ^2- m aligned & KE of translation = 1 2 m v^2= 1 2 5 (10)^2=250 ~J & Rotational kinetic energy = 1 2 / ^2= 1 2 ( 5 8 )(20)^2=125 ~J aligned aligned Total kinetic energy & = Translational + Rotational & =(250+125)=375 ~J aligned