A uniform sphere of mass $\mathrm{500 }\mathrm{g}$ rolls without slipping on a plane horizontal surface with its centre moving at a speed of $5.00 \mathrm{cm} {\mathrm{s}}^{-1}$. Its kinetic energy is:

• Correct answer
  A

  $8.75\times {10}^{-4}\mathrm{J}$
• B

  $8.75\times {10}^{-3}\mathrm{J}$
• C

  $6.25\times {10}^{-4}\mathrm{J}$
• D

  $1.13\times {10}^{-3}\mathrm{J}$

Solution

$K.E$ of the sphere $=$ Translational $K.E+$ Rotational $K.E$
$=\frac{1}{2}{mv}^2\left(1+\frac{K^2}{R^2}\right)\mathrm{}K=$ Radius of gyration
$= \frac{1}{2}\times \frac{1}{2}\times {\left(\frac{2}{100}\right)}^2\left(1+\frac{2}{5}\right)$
$= \frac{35}{4}\times {10}^{-4} \mathrm{J}$
$\mathrm{=\; 8.75}\times {10}^{-4}\mathrm{J}$

Hence, the correct answer is option: 'A'.