Two identical discs are moving with the same kinetic energy. One rolls and the other slides. The ratio of their speeds is

Step-by-step solution

According to the question, Kinetic energy for the rolling disc, or aligned KE _r= & 1 2 m v₁^2+ 1 2 I ^2 & ( Moment of inertia, I= m R^2 2 ) & = 1 2 m v₁^2+ 1 2 m R^2 2 ( v₁ R )^2 aligned Given, KE of rolling disc = KE of sliding disc or, aligned 3 4 m v₁^2= 1 2 m v₂^2 & or v₁^2 v₂^2 = 2 3 v₁ v₂ & = 2 3 or v₁: v₂ & = 2 : 3 aligned