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  4. Of the following quantities, which one has dimensions different from the remaining three ?

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Q. Of the following quantities, which one has dimensions different from the remaining three ?

AIPMTAIPMT 1989Physical World, Units and Measurements

Solution:

Dimensions of energy $E=[ML^2 T^{-2}]$
Dimensions of volume $v=[L^3]$
Dimensions of force $F=[MLT^{-2}]$
Dimensions of area $A=[L^2]$
Dimensions of voltage $V=[ML^2T^{-3}A^{-1}]$
Dimensions of charge $q=[AT]$
Dimensions of angular momentum $L=[ML^2T^{-1}]$
$\therefore $ Dimensions of $ \frac{E}{v}=\frac{[ML^2T^{-2}]}{[L^3]}=[ML^{-1}T^{-2}]$
Dimensions of $\frac{F}{A}=\frac{[MLT^{-2}]}{[L^2]}=[ML^{-1}T^{-2}]$
Dimensions of $\frac{V_q}{v}=\frac{[ML^2T^{-3}A^{-1}][AT]}{[L^3]}=[ML^{-1}T^{-2}]$
Dimensions of angular momentum is $[ML^2T^{-1}]$
while other three has dimensions $[ML^{-1}T^{-2}]$