Question

Distance(x) travelled by a particle depends on time t as x=alpha.t+beta.The dimension of alpha/beta is?

Answer 1

Answer:

the dimensions will be T^-1

Answer 2

Solution:

Distance (x) travelled by a particle depends on time t as:

$x = \alpha t + \beta$

According to Principle of Homogeneity, two terms can be added or substracted only when they have same dimensional formula.

So,  the dimension of $x$ is equal to the dimension of $\alpha t$ and also equal to the dimension of $\beta$.

Dimension of distance (x) = L

$\alpha t$ = L

$\alpha = \frac{L}{T}$

The dimension of $\alpha = LT^{-1}$

Similarly, the dimension of $\beta = L$

The dimension of  $\frac{\alpha}{\beta} = \frac{LT^{-1}}{L}$

Hence, the dimension of  $\frac{\alpha}{\beta} = T^{-1}$