First slide

Dimensions of physical quantities

Question

If the energy ( $E$ ), velocity ( $v$ ) and force ( $F$ ) be taken as fundamental quantities, then the dimensions of mass will be

Moderate

A

$[{Fv}^{- 2}]$
B

$[{Fv}^{- 1}]$
C

$[{Ev}^{- 2}]$
D

$[{Ev}^{2}]$

Solution

Let,
$E^{a} v^{b} F^{c} \propto m$
Then,
${[{ML}^{2} T^{- 2}]}^{a} {[{LT}^{- 1}]}^{b} {[{MLT}^{- 2}]}^{c} = [M]$
Equating the powers, we get
a=1, b=-2 and c=0

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