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Multiple choice physics turning effects of forces the turning effect of a force moment of force or torque couple

A solid sphere rolls on horizontal surface without slipping. What is the ratio of its rotational to translation kinetic energy.

  1. $\dfrac {2}{5}$
  2. $\dfrac {5}{2}$
  3. $\dfrac {3}{2}$
  4. $0$
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A Correct answer
Explanation

For a solid sphere rolling without slipping, rotational kinetic energy is (1/2) I w^2 where I = (2/5) M R^2, and translational kinetic energy is (1/2) M v^2. Since v = w R, rotational kinetic energy is (1/5) M v^2 and translational is (1/2) M v^2. Their ratio is (1/5) / (1/2) = 2/5.