Question

the position of a particle moving along the x axis is given by x= at + bt^2 + ct^3, where t is the time and a,b,c are constants. The dimensional formula of [abc] is

Answer 1

As we can add physical quantities of same dimensions only so a, bt2, ct3 and dt4 should have dimensions of length [L] as it is equal to the distance covered.

1. Now, a has no other quantity so it should have dimension to Length [L].

2. b has to my multiplied by t2 so it should have those dimensions that after multiplying by time twice its dimension there should be only length dimension left.

                             Dimension of bt2 is [L]=[LTa][T2]

                                                           [L]=[LTa+2]

                             Now                      a+2=o                              (so that there is only dimension of length left)

                                                         a=-2

           So, dimension of b is [LT-2].

3.  By applying same method, we can find the dimension of c is [LT-3] and of d is [LT-4].