Question

When a sphere rolls without slipping, the ratio of its translational kinetic energy to its total energy is

Answer 1

Without slipping case:

 v(velocity)= rw where w=angular velocity. 

 Moment of inertia( I )of solid sphere is 2/5 ×m×r^2 

Rotational KE of solid sphere= 1/2×I×w² = 1/2×2/5×m×r²×w²= 1/5×m×r²×w²

Translational(Linear) KE = 1/2 mv²= 1/2 m×r²×w² 

Total KE=rotational+translational=7/10×m×r²×w² 

 Ratio of translational KE/total KE = 5/7

When a sphere rolls without slipping, the ratio of its translational kinetic energy to its total energy is 5/7