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)?
k√ρrs
k√ρr3s
k√ρ2rs
k√ρr3s2
A
k√ρ2rs
B
k√ρr3s2
C
k√ρrs
D
k√ρr3s
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Solution
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The correct option is Ck√ρr3s T=krxρysz T→T,r→L,ρ→ML−3,S→MT−2 S=Fl=mal=mS2 T1=KLx(ML−2)y(MT−2)z ⇒T1=KLx−3yMy+zT−2z −2z=1⇒z=−12,y+z=0y=−z=+12 x−3y=0⇒x=3y=32 T=K63/2ρ1/2s−1/2=K√ρr3S
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