MCQ
A sphere of mass $50\,gm$ and diameter $20\,cm$ rolls without slipping with a velocity of $5\,cm/sec$ . Its total kinetic energy is
- A$625\,ergs$
- B$250\,ergs$
- ✓$875\,ergs$
- D$875\,joules$
✓
Answer
Correct option: C.
$875\,ergs$
c
$\mathrm{KE}=\frac{1}{2} \mathrm{m}\left(1+\frac{\mathrm{K}^{2}}{\mathrm{R}^{2}}\right) \mathrm{v}^{2}=\frac{1}{2} \mathrm{m}\left(1+\frac{2}{5}\right) \mathrm{v}^{2}$
$\mathrm{KE}=\frac{1}{2} \mathrm{m}\left(1+\frac{\mathrm{K}^{2}}{\mathrm{R}^{2}}\right) \mathrm{v}^{2}=\frac{1}{2} \mathrm{m}\left(1+\frac{2}{5}\right) \mathrm{v}^{2}$
$=\frac{1}{2} \times 50 \times \frac{7}{5} \times(5)^{2}=875 \mathrm{erg}$
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