Dimensional analysis of the equation v e l o c i t y x = p r e s s u r e d i f f e r e n c e 3 / 2 × d e n s i t y - 3 / 2 , gives the value of x as _______.

( v e l o c i t y ) x = P 3 / 2 × ρ - 3 / 2 = P ρ 2 = M L - 1 T - 2 M L - 3 3 2 = L 2 T - 2 3 / 2 = L 3 T - 3 = [ L 1 T - 1 ] 3 But L 1 T - 1 is the dimension of velocity. ⇒ x = 3

Physics - Unit & Dimension Question with Solution | TestHub

PhysicsUnit & DimensionMiscellaneousEasy2 minPYQ_2020

PhysicsEasynumerical

Dimensional analysis of the equation
${(v e l o c i t y)}^{x} = {(p r e s s u r e d i f f e r e n c e)}^{3 / 2} \times {(d e n s i t y)}^{- 3 / 2}$ ,
gives the value of $x$ as _______.

Answer:

3.00

Solution:

${(v e l o c i t y)}^{x} = P^{3 / 2} \times ρ^{- 3 / 2} = {(\frac{P}{ρ})}^{2}$
$= {\frac{[{M L}^{- 1} T^{- 2}]}{[{M L}^{- 3}]}}^{\frac{3}{2}}$
$= {[L^{2} T^{- 2}]}^{3 / 2}$
$= [L^{3} T^{- 3}]$
$= {[L^{1} T^{- 1}]}^{3}$
But $[L^{1} T^{- 1}]$ is the dimension of velocity.
$\Rightarrow x = 3$

Stream:NTA_ABHYASSubject:PhysicsTopic:Unit & DimensionSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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