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Question

A drop of liquid of diameter 2.8 mm breaks up into 125 identical drops. The change in energy is nearly (S.T. of liquid = 75 dynes/cm)


A

zero

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B

19 erg

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C

46 erg

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D

74 erg

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Solution

The correct option is D

74 erg


Step1: Given data

A drop of liquid of diameter 2.8 mm breaks up into 125 identical drops, R=2.82mm=1.4mm=0.14cm,n=125

Surface tension of liquid = 75 dynes/cm.

Step2: Formula used

Volumebig-drop=nVolumesmall-drop[n=numberofthesmalldrop]Changeinenergy=Surfacetenison×Increasedarea

Step3: Calculating the change in energy

The volume of the big drop is equal to the total volume of all the small drops. From this concept, the radius of each small drop can be calculated. And, the radius will help to measure the area.

Volumebig-drop=nVolumesmall-drop43πR3=n×43πr3[R=raidusofbigdrop,r=radiusofsmalldrop]43π(0.14)3=125×43πr3r=R5=0.145=0.028cmChangeinenergy=Surfacetension×increasedareaE=75×[125×4πr2-4πR2]ergE=75×4π[125×(0.028)2-(0.14)2]ergE=73.89erg74erg

The energy is nearly 74 erg.

Hence, option D is the correct option.


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