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

 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

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