Question

$P = \frac{b - {x}^{2} }{at}$

P = Power ,

$Dimensional \: Formula \: of \: Power = M {L}^{2} \: { T}^{ - 3}$


x = Distance

Dimensional Formula of Distance = L¹

t = time

Dimensional formula of time = T¹


Find the Dimensions of ( a × b )

Class 11 || Physics || Chapter 2 : Units and Measurements

Answer 1

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Answer 2

$Answer -$

Given,

$p = \frac{b - {x}^{2} }{at}$

$p - \frac{b - {x}^{2} }{at} = 0$

$p - \frac{b}{at} - \frac{ {x}^{2} }{at} = 0$

Now, By the principle of homogenity :

$\frac{ {x}^{2} }{at} = M \: {L}^{2} \: {T}^{ - 3}$

$\frac{ {L}^{2} }{a} = M \: {L}^{2} \: {T}^{ - 2}$

$a = {M}^{ - 1} \: {L}^{0} \: {T}^{ 2}$

Also,

$\frac{b }{at} = M \: {L}^{2} \: {T}^{ - 3}$

$b = (M \: {L}^{2} \: {T}^{ - 2} )\: ({M}^{ 1} \: {L}^{0} \: {T}^{ 2} )$

$b = {M}^{ 0} \: {L}^{2} \: {T}^{ 0}$

So, a × b =

$a \times b = {M}^{ - 1} \: {L}^{2} \: {T}^{ 2}$