Question

A solid sphere of mass $5\, kg$ rolls on a plane surfaces. Find its kinetic energy at an instant when its centre moves with speed $4 \,m / s$.

• A. 56 J
• B. 45 J
• C. 75 J
• D. 105 J

Answer 1

Answer: (A)

56 J

Answer 2

As we know, the rotational kinetic energy of a body is given by,
$KE =\frac{1}{2} m v^{2}\left[1+\frac{k^{2}}{R^{2}}\right]$
where, $k=$ radius of gyration
Given, $m=5 \,kg , v=4 \,m / s$ and $k=\sqrt{\frac{2}{5}} \,R$
Hence, $KE =\frac{5}{2} \times 4^{2}\left[1+\frac{2}{5}\right]$
$\Rightarrow \,KE =40 \times \frac{7}{5}=56 \,J$