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Q9. Velocity v of sound in a gas depends on the pressure P and density ρ of the gas. Using dimensional analysis, establish a relation between v and ρ. Need step by step solution. |
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Answer» ANSWERV∝P a ρ b From the relation, using dimensional ANALYSIS,Dimension of LHS= Dimension of RHS∴LT −1 =[ML −1 T −2 ] a [ML −3 ] b ⇒LT −1 =M a+b L −a−3b T −2a Comparing LHS and RHS,a+b=0−a−3b=1−2a=−1On solving the equations, a= 21 & b= 21 ∴V∝P 21 ρ − 21 ⇒V∝ ρp PLS FOLLOW me i will follow back |
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