First slide

Dimensions of physical quantities

Question

A quantity x is given by $(I F v^{2} / W L^{4})$ in terms of moment of inertia I, force F, velocity $ν$ , work W and length L. The dimensional formula for x is same as that of:

Moderate

A

Planck’s constant
B

Energy density
C

force constant
D

Coefficient of viscosity

Solution

$[\frac{I F V^{2}}{W L^{4}}] = \frac{[M L^{2}] [M L T^{- 2}] {[L T^{- 1}]}^{2}}{[M L^{2} T^{- 2}] {[L]}^{4}} = [M L^{- 1} T^{- 2}] = [E n e r g y d e n s i t y]$
This is equivalent to energy per unit volume, called as energy density

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