A force F is given by F=a t+b t^2 , where, t is time. What are the...

A force

F

is given by

F=a t+b t^2

, where,

t

is time. What are the dimensions of

a

and

b

Options

A $\left[\mathrm{MLT}^{-1}\right]$ and $\left[\mathrm{MLT}^0\right]$
B $\left[\mathrm{MLT}^{-3}\right]$ and $\left[\mathrm{ML}^2 \mathrm{~T}^4\right]$
C $\left[\mathrm{MLT}^{-4}\right]$ and $\left[\mathrm{MLT}^1\right]$
D $\left[\mathrm{MLT}^{-3}\right]$ and $\left[\mathrm{MLT}^{-4}\right]$

Correct answer

D. $\left[\mathrm{MLT}^{-3}\right]$ and $\left[\mathrm{MLT}^{-4}\right]$

Step-by-step solution

Force

F=a t+b t^2

From principle of homogeneity, Dimensions of

a t=

dimensions of

F

\therefore

Dimensions of

a=\frac{[F]}{[t]}=\frac{\left[\mathrm{MLT}^{-2}\right]}{[\mathrm{T}]}

=\left[\mathrm{MLT}^{-3}\right]

Similarly, dimensions of $b=\frac{[F]}{\left[t^2\right]}=\frac{\left[\mathrm{MLT}^{-2}\right]}{\left[\mathrm{T}^2\right]}=\left[\mathrm{MLT}^{-4}\right]

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