Question

We use $tan\theta =\frac{rg}{v^2}$ where r is radius of the curved path, $g$ is the acceleration due to gravity and $v$ is the velocity of the automobile. Which of the following is correct about the relationship?

• A. Only dimensionally correct
• B. Only numerically correct
• C. Both dimensionally and numerically correct
• D. None of these

Answer 1

Answer: (A)

Only dimensionally correct

Actual formula for banking (Using Free Body Diagram),

$tan\theta =\frac{v^2}{rg}$

Since $tan\theta$ is dimensionless either $\frac{v^2}{rg}or\frac{rg}{v^2}$ will be dimensionally correct but not numerically.

Hence, option A is correct.