Question

If $L,M$ and $p$ denotes the angular momentum, mass, and linear momentum respectively of a particle. Which of the following can represent the kinetic energy of the particle moving in a circle of radius R?

• A. $\frac{L^2}{2M}$
• B. $\frac{p^2}{M}$
• C. $\frac{L^2}{2M{R}^2}$
• D. $\frac{1}{2}Mp$

Answer 1

The correct option is C $\frac{L^2}{2M{R}^2}$

$KE=(M\times v^2)/2$
$L=M\times v\times R$
$p=M\times v$
$K.E=p^2/(2\times M)$
$K.E=L^2/(2\times M\times R^2)$