Question

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 ?
A. It is both dimensionally as well as numerically correct.
B. It is neither dimensionally correct correct.
C. It is dimensionally correct but not numerically.
D. It is numerically correct but not dimensionally.

Answer 1

Correct Answer - A
Here , `[ tan theta] = [(V^(2))/( rg)] = 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.