Question

[ML^2T^-2] is the dimensional formula for (1 Point) [a] moment of inertia, [b] pressure, [c] power, [d] density

Answer 1

Given :-

$\sf[M {}^{1} L {}^{2} T {}^{ - 2} ]$ is the dimensional formula for :-

Solution:-

Let's try to check the four options of their dimensional formulae

Moment of inertia :-

Moment of inertia is [Mass] × [Radius of gyration]²

$\: \: \sf \: D imensional \: formula \: for \: \pink{Mass} \: is \: \pink{[M {}^{1} ]}$

$\: \: \sf \: D imensional \: formula \: for \: \pink{ Radius \: of \: gyration} \: \: is \: \pink{ [ L {}^{1} ]}$

So,

$\sf \: M oment \: of \: inertia \: = [M {}^{1} ][ L {}^{1} ] {}^{2}$

$\boxed{ \sf \red{\: M oment \: of \: inertia \: = [M {}^{1} L {}^{2} ]}}$

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Pressure :-

$\sf{Pressure = \dfrac{force}{area} }$

$\: \: \sf \: D imensional \: formula \: for \: \pink{force} \: is \: \pink{[M {}^{1} L {}^{1} T {}^{ - 2} ]}$

$\: \: \sf \: D imensional \: formula \: for \: \pink{Area} \: is \: \pink{ [L {}^{2} ]}$

Substituting the values,

$\sf{Pressure = \dfrac{[M {}^{1} L {}^{1} T {}^{ - 2} ]}{{[ L^2]}} }$

$\sf{Pressure = {[M {}^{1} L {}^{1} T {}^{ - 2} ]}{{[ L {}^{ - 2} ]}} }$

$\sf{Pressure = {[M {}^{1} L {}^{1} T {}^{ - 2} ]}{ L {}^{ - 2} ]} }$

$\boxed{ \red{ \sf{Pressure = {[M {}^{-1} L^{-1} T {}^{ - 2} ]}}}}$

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Power :-

Power is (F×V) where, F = force, V= velocity.

$\: \: \sf \: D imensional \: formula \: for \: \pink{Force} \: is \: \pink{[M {}^{1} L {}^{1} T {}^{ - 2} ]}$

$\: \: \sf \: D imensional \: formula \: for \: \pink{Velocity} \: is \: \pink{ [L {}^{1} T {}^{ - 1} ]}$

$\sf \: Power = F \times V$

$\sf \: Power = [M {}^{1} L {}^{1} T {}^{ - 2} ] [L {}^{1} T {}^{ - 1} ]$

$\sf \: Power = [M {}^{1} L {}^{1 + 1} T {}^{ - 2 - 1} ]$

$\boxed{ \red{ \sf \: Power = [M {}^{1} L {}^{2} T {}^{ - 3} ] }}$

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Density :-

$\sf \: Density = \dfrac{Mass}{volume}$

$\: \: \sf \: D imensional \: formula \: for \: \pink{mass} \: is \: \pink{[M {}^{1} ]}$

$\: \: \sf \: D imensional \: formula \: for \: \pink{Volume} \: is \: \pink{ [L {}^{3} ]}$

$\sf \: Density = \dfrac{[M {}^{1} ]}{ [L {}^{3} ]}$

$\boxed{ \red{\sf \: Density = {[M {}^{1} }{ L {}^{ - 3} ]} }}$

Since there is no correct option.