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 ( n o

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 ( n of the drop, density ( ρ ) and surface tension (5) of the liquid. Which among the following will be a possible expression for T (where, k is a dimensionless constant)?

TestHub · Accepted Answer

According to the question. time period. T α r a p b s c r = k r a p b s c Thus, putting dimension, we get Equating the dimensions of both sides, we get [ T ] = [ L ] a [ ML − 3 ] b [ MT − 2 ] c [ T ] = [ M ] b + c ⋅ [ L ] 2 a − 3 b [ T ] − 2 c b + c = 0 , a − 3 b = 0 and − 2 x = c = − 2 1 ​ b = 2 1 ​ a = 3 b = 2 3 ​ ​ Putting these value of a , b and c into Eq. (i), we get T = k ⋅ r 2 3 ​ p 2 1 ​ ⋅ s − 2 1 ​ = k s ρ ​ r 3 ​

Physics - Unit & Dimension Question with Solution | TestHub

Options:

Doubts & Discussion