Question Detail
Question
In the equation F = A sin(Ct), where F is force and t is time, what are the dimensions of A and C respectively?
Correct Answer
Option A is the correct answer.
Detailed Explanation
The argument of a trigonometric function (Ct) must be dimensionless. Therefore, [C][t] = 1, so [C] = 1/[t] = T⁻¹. The function sin(Ct) is also dimensionless. Therefore, [A] must have the same dimensions as F, which is force, so [A] = [F] = MLT⁻².
Hint
The argument of a sine function must be dimensionless. The value of a sine function is also dimensionless.