Question:
A sphere of diameter $0.2\,m$ and mass $2\, kg$ is rolling on an inclined plane with velocity $ \upsilon =0.5\, m/s$. The kinetic energy of the sphere is:
A sphere of diameter $0.2\,m$ and mass $2\, kg$ is rolling on an inclined plane with velocity $ \upsilon =0.5\, m/s$. The kinetic energy of the sphere is:
Updated On: Nov 12, 2025
- 0.1 J
- 0.3 J
- 0.5 J
- 0.42 J
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The Correct Option is D
Solution and Explanation
The kinetic energy of sphere while rolling on an inclined plane is given by
$ E_{K}= $ Translational kinetic energy $+$ Rotational kinetic energy
$=\frac{1}{2} m v^{2}+\frac{1}{2} I \omega^{2}$
$E_{K}=\frac{1}{2} \times 2 \times(0.5)^{2}+\frac{1}{2} \times\frac{2}{3} \times 2 \times(0.1)^{2} \times\left(\frac{0.5}{0.1}\right)^{2}$
$=0.25+0.17=0.42 J$
$ E_{K}= $ Translational kinetic energy $+$ Rotational kinetic energy
$=\frac{1}{2} m v^{2}+\frac{1}{2} I \omega^{2}$
$E_{K}=\frac{1}{2} \times 2 \times(0.5)^{2}+\frac{1}{2} \times\frac{2}{3} \times 2 \times(0.1)^{2} \times\left(\frac{0.5}{0.1}\right)^{2}$
$=0.25+0.17=0.42 J$
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
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