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JIPMER 2005
Exam
JIPMER
Year
2005
Subject
Physics
Chapter
Rotational Motion

JIPMER 2005 · Physics · Rotational Motion

A sphere of diameter 0.2 m and mass 2 kg is rolling on an inclined...

A sphere of diameter 0.2 m and mass 2 kg is rolling on an inclined plane with velocity v=0.5 m/sv=0.5 \mathrm{~m} / \mathrm{s}. The kinetic energy of the sphere is

Options

  1. A0.1 J
  2. B0.3 J
  3. C0.5 J
  4. D0.42 J

Correct answer

D. 0.42 J

Step-by-step solution

The kinetic energy of sphere while rolling on an inclined plane is given by EK= Translational kinetic energy +extRotationalkineticenergyE_K=\text{ Translational kinetic energy }+ ext{ Rotational kinetic energy}=12mv2+12Iω2EK=12×2×(0.5)2+12×23×2×(0.1)2×(0.50.1)2=0.25+0.17=0.42J\begin{aligned}= & \frac{1}{2} m v^2+\frac{1}{2} I \omega^2 \\ E_K= & \frac{1}{2} \times 2 \times(0.5)^2+\frac{1}{2} \times \frac{2}{3} \times 2 \times(0.1)^2 \times\left(\frac{0.5}{0.1}\right)^2 \\ = & 0.25+0.17=0.42 \mathrm{ J}\end{aligned}$$
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