Q. The relation $\tan \theta=v^{2} / r g$ 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?

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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.

Solution:

Here, $[\tan \theta]=\left[\frac{v^{2}}{r g}\right]=M^{0} L^{0} T^{0}$.
Also, in actual expression for the angle of banking of a road, there is no numerical factor involved.
Therefore, the relation is both numerically and dimensionally correct.

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