Question

The relation $tan\theta =v^2/rg$ gives the angle of banking of the cyclist going round the curve. Here v is the speed of the cyclist, r is the radius of the curve, and g is the acceleration due to gravity. Which of the following statements about the relation is true?

• A. It is both dimensionally as well as numerically correct.
• B. It is neither dimensionally correct nor numerically correct.
• C. It is dimensionally correct but not numerically.
• D. It is numerically correct but not dimensionally.

Answer 1

The correct option is A It is both dimensionally as well as numerically correct.

Angle of banking $=\frac{V^2}{rg}$ is

true equation,

Now,

Checking its diamensions

$\left[O\right]=\frac{{\left(m/s\right)}^2}{m\left(m/s^2\right)}=\frac{\left[L^2{T}^{-2}\right]}{L\left[{LT}^{-2}\right]}$

$\left[O\right]=\left[O\right]$