Question

A body having moment of inertia about its axis of rotation equal to $3kg{m}^2$ is rotating with angular velocity equal to $3rad/s$. Kinetic energy of this rotating body is the same as that of a body of mass $27kg$ moving with a speed of :

• A. $1.0m/s$
• B. $0.5m/s$
• C. $1.5m/s$
• D. $2.0m/s$

Answer 1

Answer: (A)

$1.0m/s$

$\begin{array}{c}\omega =3rad/S\\ I=3kg{m}^2\end{array}|\begin{array}{c}m=27kg\\ \nu \end{array}$ (given and assumed analogous data from question)

$\frac{1}{2}I{\omega }^2=\frac{1}{2}m{\nu }^2$ (as both the energies are equal)

$\frac{1}{2}\times 3\times 9=\frac{1}{2}\times 27\times {\nu }^2$

$\nu =1m/s$