Question

A solid sphere is rolling purely on a horizontal surface. The angular velocity of sphere about its central axis is 2 $\frac{rad}{s}$ and it has m = 4 kg and R = 2m. What is the total kinetic energy of the sphere?

• A. $\frac{148}{5}J$
• B. $\frac{124}{5}J$
• C. 100 J
• D. 25 J

Answer 1

The correct option is B $\frac{124}{5}J$

Total kinetic energy = $\frac{1}{2}m{V}_{cm}^2+\frac{1}{2}I{\omega }^2$
$I=\frac{2}{5}m{R}^2=\frac{2}{5}\times 4\times (2{)}^2$
$=\frac{32}{5}kg-m^2$
$V=R\omega$
$V=2\times 2=4\frac{m}{s}$
T.K.E $=\frac{1}{2}\left(4\right)(4{)}^2+\frac{1}{2}\times \frac{32}{5}\times (2{)}^2$
$=32+\frac{64}{5}=\frac{160+64}{5}=\frac{124}{5}J$