Q. Given that $\upsilon$ is speed, $r$ is the radius and $g$ is the acceleration due to gravity. Which of the following is dimensionless
A) $\upsilon^{2}/rg$
B) $\upsilon^{2}r/g$
C) $\upsilon^{2}g/r$
D) $\upsilon^{2}rg$
Explanation
Angle of banking: $\tan\theta = \frac{v^{2}}{rg}$. i.e. $\frac{v^{2}}{rg}$ is dimensionless
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.