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Physics
Which of the following is dimensionless?
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Q. Which of the following is dimensionless?
NTA Abhyas
NTA Abhyas 2022
A
$\frac{v^{2}}{r g}$
B
$\frac{v^{2} g}{r}$
C
$\frac{v g}{r}$
D
$v^{2}rg$
Solution:
We know that for a particle falling through a height $r$ , the speed is
$v=\sqrt{2 g r}$
$v^{2}=2gr$
$\frac{v^{2}}{g r}=2$