Question

The angle of banking `theta` for a cyclist taking a turn on a curved road of radius r, with a velocity v is given by tan `theta=(v^(n))/(rg)`. What is the value of n?
A. 1
B. 3
C. 2
D. 4

Answer 1

Correct Answer - c
`tantheta=(v^(n))/(rg) therefore [tantheta]=[(v^(n))/(rg)]`
The trignometrical ratio tan `theta` has no dimensions and is represented as `[L^(0)M^(0)T^(0)]`
`[L^(0)M^(0)T^(0)]=([L^(1)T^(-1)]^(n))/([L^(1)L^(1)T^(-2)])=([L^(1)T^(-1)]^(n))/([L^(1)T^(-1)]^(2))`
`therefore [L^(1)T^(-1)]^(n)=[L^(1)T^(-1)]^(2) therefore n=2`
`therefore` The correct relation is tan `theta=(v^(2))/(rg)`.