Question

A sphere of diameter $0.2\, m$ and mass $2\, kg$ is rolling on an inclined plane with velocity $ v=0\, . 5\, m/s.$ The kinetic energy of the sphere is:

• A. 0.1 J
• B. 0.3 J
• C. 0.5 J
• D. 0.42 J

Answer 1

The Correct Option is D

The kinetic energy of sphere while rolling on an inclined plane is given by $E_{ K }$ =Translational kinetic energy + Rotational kinetic energy $= \frac{1}{2} m v^{2}+\frac{1}{2} I \omega^{2}$ $E_{K}=\frac{1}{2} \times 2 \times(0.5)^{2}+\frac{1}{2} \times \frac{2}{3} \times 2 \times$ $(0.1)^{2} \times\left(\frac{0.5}{0.1}\right)^{2}$ $=0.25+0.17=0.42\, J$