Question

the position of a particle varies with time is given by X = a + b t then the dimension of a b will be

Answer 1

HELLO THERE!

Here's your answer :)

Position of the particle with time is given by the equation X = a + bt

According to the principle of homogeneity, two quantities can be added only if they have the same dimensions. Also, an equation is valid when the dimensions of left hand side is equal to the dimensions of right hand side.

For example, you cannot add area and length (addition of 4 cm + 2 cm² is not possible).

Given equation is X = a + bt.

Dimensions of position [X] = [L]

So, Dimensions of a + bt = [L] (then only the equation will be valid).

Also, Dimensions of a = Dimensions of bt.

So, [bt] = [L]

We know, that dimensions of time t is [T].

So, b [T] = [L].

=> b = [L T⁻¹] (hence, we get the dimensions of b).

Now, dimensions of a should be equal to dimensions of bt, and dimensions of bt = [L T⁻¹].[T] = [L].

So, dimensions of a = [L].

So, your answer is:

Dimensions of a = [L]

Dimensions of b = [L T⁻¹]

HOPE MY ANSWER IS SATISFACTORY..

THANKS!