KVPY SX SB Exam 2012 Question Paper

Question : 23 of 120

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A liquid drop placed on a horizontal plane has a near spherical shape (slightly flattened due to gravity). Let R be the radius of its largest horizontal section. A small disturbance causes the drop to vibrate with frequency v about its equilibrium shape. By dimensional analysis the ratio

v/√{σ\/{ ρR^3}}

, can be (Here σ is surface tension, ρ is density, g is acceleration due to gravity, and k is an arbitrary dimensionless constant.)

${kρgR^2}/σ$
${kρR^2}/{gσ}$
${kρR^3}/{gσ}$
${kρ}/{gσ}$

Validate

Solution:

v/√{σ\/{ ρR^3}}

is dimensionless

{kρgR^2}/σ

is also dimensionless

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