Question

A solid sphere of mass 0.5 kg and radius 0.1 m rolls without slipping with velocity $0.2m{s}^{-1}$ The total kinetic energy of the sphere is:

• A. 0.14 J
• B. 0.28 J
• C. 0.014 J
• D. 0.028 J

Answer 1

The correct option is C 0.014 J

Solution

Since it is pure rolling,

$V=\omega R$

$\Rightarrow \omega =\frac{V}{R}=\frac{0.2}{0.1}=2$ rad/s

$K{E}_{Translational}=\frac{1}{2}m{v}^2=\frac{1}{2}\times \frac{1}{2}\times (0.2{)}^2$

$={10}^{-2}J$

$K{E}_{Rotational}=\frac{1}{2}J{\omega }^2=\frac{1}{2}\left(\frac{2}{5}M{R}^2\right){\omega }^2$

$=\frac{\left(\frac{1}{2}\right)(0.1{)}^2}{5}(2{)}^2=4\times {10}^{-3}J$

$K{E}_{Total}=K{E}_{Translational}+K{E}_{rotational}$

$={10}^{-2}J+4\times {10}^{-3}J$

$=0.014J$

Option - C is correct.