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NEET 2003
Exam
NEET
Year
2003
Subject
Physics
Chapter
Rotational Motion

NEET 2003 · Physics · Rotational Motion

A ball rolls without slipping. The radius of gyration of the ball...

A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is KK. If radius of the ball be RR, then the fraction of total energy associated with its rotational energy will be:

Options

  1. AK2+R2R2\frac{K^2+R^2}{R^2}
  2. BK2R2\frac{K^2}{R^2}
  3. CK2K2+R2\frac{K^2}{K^2+R^2}
  4. DR2K2+R2\frac{R^2}{K^2+R^2}

Correct answer

C. K2K2+R2\frac{K^2}{K^2+R^2}

Step-by-step solution

Total energy =12\frac{1}{2} I \omega^2+12\frac{1}{2} m v^2 =12\frac{1}{2} m v^2 \left(1+\frac{K^2}{R^2}\right)Rotational energy =12Iω2=K2+R21+K2R2\begin{aligned} & \text{Rotational energy }=\frac{1}{2} I \omega^2 \\ & =\frac{K^2+R^2}{1+\frac{K^2}{R^2}} \end{aligned}Required fraction =K2/R21+K2/R2=K2R2+K2\begin{aligned} & \text{Required fraction }=\frac{K^2 / R^2}{1+K^2 / R^2} \\ & =\frac{K^2}{R^2+K^2} \end{aligned}$$
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