Problem 5: (a) Suppose that the displacement of an object is related to time according to the expression x=Bt². What are the dimensions of B?

(b) A displacement is related to time as x = Asin(2πft), where A and f are constants. Find the dimensions of A?

Solution

(a)                   Given data:       x = displacement

                                                t = time

                        Required:          Dimensions of B in x = Bt²

Given that

Therefore,

(b)                   Given data:       x= displacement

Angle = 2πft

Required : Dimensions of A in x = Asin(2πft)

Since

Therefore,

Now sin(2πft) is the ratio between two similar quantities, i-e, lengths (length of perpendicular/ length of hypotenuse), therefore, it has no dimensions.

Hence