Question

Write the dimension of a / b in the x = at + bt2. Where x is the distance and t is the time?​

Answer 1

The dimension of a/b where x is the distance and t is the time is T

Given the expression

x = at + bt²

where

x is the distance

t is the time

Based on the homogeneity principle, the expression on the left-hand side must be equal to that on the right. Hence;

x = at

`a = (x)/(t)`

Since x is the distance and distance is measured in metres, the dimension equivalent will be the length 'L'

Since t is the time and time is measured in seconds, the dimension equivalent will be the seconds 'T'

`a=(L)/(T)`

Similarly;

x = bt²

`b=(x)/(t^2)\\b=(L)/(T^2)`

Next is to get a/b;

`(a)/(b) = (L)/(T) / (L)/(T^2)\\(a)/(b) = (L)/(T)*(T^2)/(L) \\(a)/(b) =(T^2)/(T)\\(a)/(b) =T`

Hence the dimension of a/b is T