Question

If force acting on a particle at any time t is given by relation F = at + bt2, where, a and b are dimensional constant. The dimensional formula of a/b will be

Answer 1

Answer:

Answer is:M⁰L⁰T¹

Explanation:

By Principle of Homogeneity

Dimension of a=MLT-3

Dimension of b=MLT-4

Therefore a/b= M⁰L⁰T

Answer 2

Answer:

dimensional formula of a/b will be [T]

Explanation:

Dimensions of Force is,[F]=$MLT^{-2}$

Only quantities with similar dimensions are added and subtracted with each other. Therefore, both quantities on right side of the equation must have same dimensions as force.

Now, dimensions of [at]=[a][T]=[$MLT^{-2}$]

$\implies$ dimensions of a = [a]=$\frac{MLT^{-2}}{T}=MLT^{-3}$

similarly, dimesnsions of $[at^2]=[a][t^2]=[MLT^{-2}]$

$\implies$ dimensions of b = $\frac{MLT^{-2}}{T^2} =MLT^{-4}$

Therefore, dimesions of a/b = $\frac{[MLT^{-3}]}{[MLT^{-4}]} =[T]$

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