A quantity x is given by (IFv2 / WL4) in terms of moment of inertia I, force F, velocity v , work W and Length L. The dimensional formula for x is same as that of :

Question

A quantity x is given by (IFv2 / WL4) in terms of moment of inertia I, force F, velocity v , work W and Length L. The dimensional formula for x is same as that of : (A) Planck's constant (B) Force constant (C) Energy density (D) Coefficient of viscosity

Tardigrade Admin · Accepted Answer

x =( IFV 2/ WL 4) [ x ]=([ ML 2][ MLT -2][ LT -1]2/[ ML 2 T -2][ L ]4) [ x ]=[ ML -1 T -2] [Energy density] =[( E / V )] =[( ML 2 T -2/ L 3)] =[ ML -1 T -2] Same as x

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

Planck's constant

Force constant

Energy density

Coefficient of viscosity

$x = \frac{I F V ^{2}}{W L ^{4}}$
$[x] = \frac{[ M L ^{2} ] [ M L T ^{- 2} ] [ L T ^{- 1} ] ^{2}}{[ M L ^{2} T ^{- 2} ] [ L ] ^{4}}$
$[x] = [M L^{- 1} T^{- 2}]$
[Energy density] $= [\frac{E}{V}]$
$= [\frac{M L ^{2} T ^{- 2}}{L ^{3}}]$
$= [M L^{- 1} T^{- 2}]$
Same as $x$

Q. A quantity x is given by (IFv2/WL4) in terms of moment of inertia I, force F, velocity v, work W and Length L. The dimensional formula for x is same as that of :