A uniform thin rod of length and mass moves in a horizontal plane

PHYSICS · Single correct · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

A uniform thin rod of length

L

and mass

M

moves in a horizontal plane. At one instant its center of mass translates with speed

v

, and it rotates about an axis through the center of mass (perpendicular to the plane) with angular speed

\omega

. Which expression gives the ratio of its rotational kinetic energy to its translational kinetic energy? (a)

\dfrac{L^{2}\omega^{2}}{6\,v^{2}}

(b)

\dfrac{L^{2}\omega^{2}}{3\,v^{2}}

(c)

\dfrac{L^{2}\omega^{2}}{12\,v^{2}}

(d)

\dfrac{L^{2}\omega^{2}}{24\,v^{2}}