Question

If energy (E) , force (F) and linear momentum (P) are fundamental quantities, then match the following and give correct answer.

A	B
Physical quantity	Dimensional formula
a) Mass	d) $E^0{F}^{-1}{p}^1$
b) Length	e) $E^{-1}{F}^0{p}^2$
c) Time	f) $E^1{F}^{-1}{p}^0$

• A. a-d, b-e, c-f
• B. a-f, b-e, c-d
• C. a-e, b-f, c-d
• D. a-e, b-d, c-f

Answer 1

The correct option is C a-e, b-f, c-d

Dimensions of $E=\left[M{L}^2{T}^{-2}\right]$

Dimensions of $F=\left[ML{T}^{-2}\right]$

Dimensions of $P=\left[ML{T}^{-1}\right]$

Thus $E^0{F}^{-1}{P}^1=\left[T\right]$

$E^{-1}{F}^0{P}^2=\left[M\right]$

$E^{-1}{F}^0{P}^2=\left[L\right]$