Test if the following equation is dimensionally correct- v-12-mgIIwhere h-height- S-surface tension- - - density- P- pressure- V- volume- - - coefficient of viscosity- v- frequency and I- moment of inertia-

v=12π√((mgI/I)) LHS = dimension of v=[T^ 1] RHS =√((mgI/I))=√([M][LT^ 2][L][ML^2])=[T^ 1] LHS = RHSSo, the relation is correct. ...

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Standard XII

Physics

Dimensional Analysis

Test if the f...

Question

Test if the following equation is dimensionally correct.
$v = \frac{1}{2 π} \sqrt{\frac{m g I}{I}}$
where $h =$ height, $S =$ surface tension, $ρ =$ density, $P =$ pressure, $V =$ volume, $η =$ coefficient of viscosity, $v =$ frequency and $I =$ moment of inertia.

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Solution

$v = \frac{1}{2 π} \sqrt{(m g I / I)}$
LHS $=$ dimension of $v = [T^{- 1}]$
RHS $= \sqrt{(m g I / I)} = \sqrt{\frac{[M] [L T^{- 2}] [L]}{[M L^{2}]}} = [T^{- 1}]$
LHS $=$ RHS
So, the relation is correct.

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Test if the following equation is dimensionally correct.v=12π√mgIIwhere h=height, S=surface tension, ρ= density, P= pressure, V= volume, η= coefficient of viscosity, v= frequency and I= moment of inertia.

v=12π√(mgI/I)LHS=dimension of v=[T−1]RHS=√(mgI/I)=√[M][LT−2][L][ML2]=[T−1]LHS=RHSSo, the relation is correct.

Test if the following equation is dimensionally correct.
$v = \frac{1}{2 π} \sqrt{\frac{m g I}{I}}$
where $h =$ height, $S =$ surface tension, $ρ =$ density, $P =$ pressure, $V =$ volume, $η =$ coefficient of viscosity, $v =$ frequency and $I =$ moment of inertia.

$v = \frac{1}{2 π} \sqrt{(m g I / I)}$
LHS $=$ dimension of $v = [T^{- 1}]$
RHS $= \sqrt{(m g I / I)} = \sqrt{\frac{[M] [L T^{- 2}] [L]}{[M L^{2}]}} = [T^{- 1}]$
LHS $=$ RHS
So, the relation is correct.