Question

The kinetic energy of the system in centre of mass frame is

• A. $\frac{3}{2}m{\omega }_0^2{L}^2$
• B. $\frac{1}{2}m{\omega }_0^2{L}^2$
• C. $\frac{1}{3}m{\omega }_0^2{L}^2$
• D. $\frac{4}{3}m{\omega }_0^2{L}^2$

Answer 1

Answer: (C)

$\frac{1}{3}m{\omega }_0^2{L}^2$

As the kinetic energy will be only rotational kinetic energy in C.M. frame:

$K.E{.}_{C.M.}=\frac{1}{2}I{\omega }^2$

CM will be $\frac{L}{3}$ distance from mass $2m$ and $\frac{2L}{3}$ distance from mass $m$

$I=m(\frac{2L}{3}{)}^2+2m(\frac{L}{3}{)}^2=\frac{2}{3}m{L}^2$

$K.E.=\frac{1}{2}\frac{2}{3}m{L}^2{\omega }_{\circ }{}^2$

$K.E.=\frac{1}{3}m{L}^2{\omega }_{\circ }{}^2$