    Question

# Determine the change in volume of 6 litres of alcohol if the pressure is decreased from 200 cm of Hg to 75 cm of Hg. [Velocity of sound in alcohol is 1280 m/s density of alcohol =0.81 gm/cc, density of Hg=13.6 gm/cc and g=981 cm/s2]

A
0.5 mL
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B
0.75 mL
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C
1 mL
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D
2 mL
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Solution

## The correct option is B 0.75 mL For propagation of sound in liquid v=√(B/ρ) i.e. B=v2ρ where B is bulk modulus of liquid, v is the velocity of sound, and ρ is the density of the liquid, here alchohol. By definition B=−VΔPΔV So −VΔPΔV=v2ρal i.e. ΔV=V(−ΔP)ρalv2 Here, ΔP=H2ρHgg−H1ρHgg=(75−200)×13.6×981=−1.667×106 dynes/cm2 So, ΔV=(6×103)(1.667×106)0.81×(1.280×105)2=0.75 cc=0.75 mL  Suggest Corrections  0      Similar questions  Explore more