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Question

A spherical liquid drop is placed on a horizontal plane. A small disturbance causes the volume of the drop to oscillate. The time period of oscillation (T) of the liquid drop depends on radius (r) of the drop, density (ρ) and surface tension (S) of the liquid. Which among the following will be a possible expression for T (where k is a dimensionless constant)? (given surface tension is force per unit length)

A
kρrS
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B
kρ2rS
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C
kρr3S
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D
kρr3S2
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Solution

The correct option is C kρr3S
T=krxρySz
TT,rL,ρML3,SMT2
S=Fl=mal=ms2
T1=KLx(ML3)y(MT2)z
T1=KLx3yMy+zT2z
2z=1z=12,y+z=0,y=z=+12
x3y=0x=3y=32
T=kL3/2ρ1/2s1/2=kρr3S

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