Question

If x and y are pressure gradient and force respectively then dimension of d^3y/dx^3

Answer 1

therefore dimension of d³y/dx³ is $[M^{-2}T^7T^4]$

It is given that x and y are pressure gradient and force respectively.

we have to find the dimension of d³y/dx³

pressure gradient is the rate of change of pressure with respect to position.

so, pressure gradient, x = ∆P/∆x

then dimension of pressure gradient, x = dimension of pressure/dimension of position

= [M¹L¯¹T¯²]/[L¹] = [M¹L¯²T¯²]

again, force, y = mass × acceleration

so dimension of force, y = [M¹L¹T¯²]

then dimension of d³y/dx³ = dimension of y/dimension of x³

= [M¹L¹T¯²]/[M¹L¯²T¯²]³

= [M¯²L^7T⁴]

therefore dimension of d³y/dx³ is $[M^{-2}T^7T^4]$

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