Question

Which of the following is dimensionless?

• A. $\frac{v^2}{rg}$
• B. $\frac{v^{2}g}{r}$
• C. $\frac{vg}{r}$
• D. $v^{2}rg$

Answer 1

Answer: (A)

We know that for a particle falling through a height $r$ , the speed is
$v=\sqrt{2gr}$
$v^2=2gr$
$\frac{v^2}{gr}=2$