Topic: Comparison of linear and rotational motion· Rotational Motion

A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (K_t) as well as rotational kinetic energy (K_r) simultaneously. The ratio K_t:(K_t+K_r) for the sphere is

1. 7 : 10

2. 10 : 7

3. 5 : 7

4. 2 : 5

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Answer: 3. 5 : 7

For a solid sphere rolling without slipping, $K_t=\tfrac12mv^2$ and $K_r=\tfrac12I\omega^2=\tfrac12\cdot\tfrac25mR^2\cdot\dfrac{v^2}{R^2}=\tfrac15mv^2$.

$$\frac{K_t}{K_t+K_r}=\frac{1/2}{1/2+1/5}=\frac{5}{7}$$

Ratio is 5 : 7.

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A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (K_t) as well as rotational kinetic energy (K_r) simultaneously. The ratio K_t:(K_t+K_r) for the sphere is

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