Question

The correctness of an equation is checked
using the principle of homogeneity.
For an equation x = a + bt + ct ^2
,
where x is in metre and t in second. What will
be the dimension of ‘b’?

Answer 1

LT-1 x =L and. t = T. h. j.

Answer 2

The dimension of 'b' is found to be $[b] = [LT^{-1} ]$.

Given:

Principle of Homogeneity.

"It states that dimensions of each of the terms of a dimensional equation on both sides should be the same".

Explanation:

As, by the principle the dimension of the L.H.S = R.H.S.

Dimension of L.H.S,

[x] = [L], as, x is given in 'm'.

So, each of the individual values of R.H.S must have the dimension [L] to be added.

[a] = [L]

[bt] = [L]

$[ct^{2} ]$ = [L]

Consider [bt] = [L]

This can be written as,

[b][T] = [L], as the t is given in sec.

[b] = [L]/[T]

$[b] = [LT^{-1} ]$

Hence ,the dimension of 'b' is calculated.

To know more about use of dimensional analysis, here

https://brainly.in/question/15491011?msp_poc_exp=2

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