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KVPY2012PhysicsUnits and Dimensions

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 / R ³ can be (Here is surface tension, is density, g is acceleration due to gravity, and k is arbitrary dimensionless constant)-

Options

  1. Ak gR ² /
  2. Bk R ² / g
  3. Ck R ³ / g
  4. Dk / g

Correct answer

A. k gR ² /

Step-by-step solution

v / R ³ is dimensionless k gR ² / is also dimensionless

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