Question

The total kinetic energy of a body of mass $10 kg$ and radius $2 m$ moving with a velocity of $15 m / s$ without slipping is 40 joule. The radius of gyration is

• A. $1 \,m$
• B. $2\, m$
• C. $1.89 \,m$
• D. $1.71 \,m$

Answer 1

Answer: (C)

Total kinetic energy of the body is $\frac{1}{2} m v^{2}\left(1+\frac{K^{2}}{R^{2}}\right)$
$40=\frac{1}{2} \times 10 \times(15)^{2}\left(1+\frac{K^{2}}{(2)^{2}}\right)$
$\frac{80}{10 \times 225}=1+\frac{K^{2}}{4}$
$=0.96 \times 4=K^{2}$
$K=1.89\, m$