Properties of Matter 3 Question 7

13. A drop of liquid of radius R=102m having surface tension S=0.14πNm1 divides itself into K identical drops. In this process the total change in the surface energy ΔU=103J. If K=10α, then the value of α is

(2017 Adv.)

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Answer:

Correct Answer: 13. (a) g50

(b) gm02Aρ

Solution:

  1. (a) Mass of water =( Volume )( density )

m0=(AH)ρH=m0Aρ

Velocity of efflux,

v=2gH=2gm0Aρ=2m0gAρ

Thrust force on the container due to draining out of liquid from the bottom is given by,

F= (density of liquid) (area of hole)(velocity of efflux) 2

F=ρav2F=ρ(A/100)v2=ρ(A/100)(2m0gAρ)F=m0g50

Acceleration of the container, a=F/m0=g/50

(b) Velocity of efflux when 75 liquid has been drained out i.e. height of liquid, h=H4=m04Aρ



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