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Physics - Unit & Dimension Question with Solution | TestHub

PhysicsUnit & DimensionMiscellaneousEasy2 minQB

PhysicsEasysingle choice

The velocity $v$ of sound in a gas depends on the pressure $p$ and the density $d$ of the gas as $v = k p^{a} d^{b} (k$ dimensionless). The values of $a$ and $b$ are

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Answer:

Solution:

$[L T^{- 1}]$
$= ([M L^{- 1} T^{- 2}])^{a} ([M L^{- 3}])^{b} : - 2 a$
$= - 1 \Rightarrow a$
$= \frac{1}{2}; a + b$
$= 0 \Rightarrow b$
$= - \frac{1}{2}$ ;
check $L$ :
$- a - 3 b = - \frac{1}{2} + \frac{3}{2} = 1$ .
So $v = k \frac{p}{d}$ .

Stream:JEESubject:PhysicsTopic:Unit & DimensionSubtopic:Miscellaneous

⏱ 2mℹ️ Source: QB

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