Question

v²= ut+2gh Check this formula correct or incorrect using dimensions
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Answer 1

Given

• v² = ut + 2gh

To Find

• Dimensional correctness of the equation

Solution

☯ [MᵃLᵇTᶜ]

• This is a general way used to represent most of the physical quantities

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✭ According to the Question :

LHS :

➞ v²

➞ [M⁰L¹T⁻¹]²

➞ [M⁰L²T⁻²]

RHS :

➞ ut + 2gh

➞ [M⁰L¹T⁻¹] × [M⁰L⁰T¹] + [M⁰L¹T⁻²] × [M⁰L¹T⁰]

➞ [M⁰L¹T⁰] + [M⁰L²T⁻²]

We may observe that LHS ≠ RHS

• Also we can't add quantities of different dimensions

∴ The given equation is dimensionally incorrect

Answer 2

Answer

dimensionally incorrect

Explanation:

$v = (l ^{1} {t}^{ - 1} )^{2} = {l}^{2} {t}^{ - 2} \\ \\ ut = ( {l}^{1} {t}^{ - 1} )( {t}^{1} ) \\ \\ gh = ( {l}^{1} {t}^{ - 2} )( {l}^{1} ) \\ \\ h = height \: is \: length \\ \\ g \: is \: acceleration \: due \: to \: gravity \\ \\ 2 \: is \: numerical \: hence \: not \: counted \\ \\ ut = {l}^{1} {t}^{ - 1 + 1} = {l}^{1} \\ \\ gh = ({l}^{1 + 1 = 2} {t}^{ - 2}) = {l}^{2 } {t}^{ - 2} \\ \\ {l}^{2} {t}^{ - 2} \: \: \: is \: not \: equal \: to \: \: \: = {l}^{3} {t}^{ - 2}$

it was obtained by adding l¹+l²=l³

it was obtained by adding l¹+l²=l³for a equation to be correct dimension of LHS should be equal to dimension of RHS

it was obtained by adding l¹+l²=l³for a equation to be correct dimension of LHS should be equal to dimension of RHShere LHS≠RHS

it was obtained by adding l¹+l²=l³for a equation to be correct dimension of LHS should be equal to dimension of RHShere LHS≠RHSut+gh=l²×l¹+t–²

=l³+t–² RHS

v²=LHS

=l²t–²

=l²t–²≠l³t–²