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JIPMER 2006
Exam
JIPMER
Year
2006
Subject
Physics
Chapter
Rotational Motion

JIPMER 2006 · Physics · Rotational Motion

If a spherical ball rolls on a table without slipping the friction...

If a spherical ball rolls on a table without slipping the friction of its total energy associated with rotational energy is :

Options

  1. A3/53 / 5
  2. B2/72 / 7
  3. C2/52 / 5
  4. D3/73 / 7

Correct answer

B. 2/72 / 7

Step-by-step solution

Rotational energy of sphere ER=12Iω2E_R=\frac{1}{2} I \omega^2 For sphere, moment of inertia I=25mR2∴ER=12(25mR2)(vR)2=15mv2\begin{aligned} I & =\frac{2}{5} m R^2 \\ \therefore \quad E_R & =\frac{1}{2}\left(\frac{2}{5} m R^2\right)\left(\frac{v}{R}\right)^2 \\ & =\frac{1}{5} m v^2\end{aligned} Translational kinetic energy Er=12mv2E_r=\frac{1}{2} m v^2∴ Total energy =15mv2+12mv2=710mv2\begin{aligned} \therefore \text{ Total energy } & =\frac{1}{5} m v^2+\frac{1}{2} m v^2 \\ & =\frac{7}{10} m v^2\end{aligned}∴\therefore Required fraction =15mv2710mv2=27=\frac{\frac{1}{5} m v^2}{\frac{7}{10} m v^2} =\frac{2}{7}
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