Q. Which of the following is dimensionless?
A) $\frac{v^{2}}{rg}$
B) $\frac{v^{2}g}{r}$
C) $\frac{vg}{r}$
D) $v^{2}rg$
Explanation
The velocity of a body at highest point of vertical circle is, $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v = \sqrt{rg}$ Or $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v^{2} = rg$ Or $\frac{v^{2}}{rg} = constant$ Hence, $\frac{v^{2}}{rg}$ is dimensionless.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.