Question

A displacement is related to time as x = A sin(2?ft), where A and f are constants. Find the dimensions of A. [Hint: A trigonometric function appearing in an equation must be dimensionless.]
A. L * T
B. L / T
C. L
D. T / L
E. T

Answer 1

Answer:

The right option is C. i.e L

Explanation:

Dimension of a quantity is the collection of the indexes of each of the fundamental quantities contained in it.

Therefore, to get the dimension of A in the equation

X=Asin(2(pi)ft)

Making A the subject of the formula

A = X / (sin(2(pi)ft)

Since sin(2(pi)ft which is a trigonometric function does not have a dimension

A = L

The dimension of A is L