The time period ( T ) of small oscillations of the surface of a liquid drop depends on its surface tension ( s ), the density ( ρ ) of the liquid and it's mean radius ( r ) as T = c s x ρ y r z .

Question

The time period ( T ) of small oscillations of the surface of a liquid drop depends on its surface tension ( s ), the density ( ρ ) of the liquid and it's mean radius ( r ) as T = c s x ρ y r z . If in the measurement of the mean radius of the drop, the error is 2 %, the error in the measurement of surface tension and density both are of 1 % . Find the percentage error in measurement of the time period.

TestHub · Accepted Answer

T = c s x ρ y r z [ T ] = [ s ] x [ ρ ] y [ r ] z = [ M T − 2 ] x [ M L − 3 ] y [ L ] z ⇒ [ T ] = M x + y L − 3 y + z T − 2 x x + y = 0 − 2 x = 1 ⇒ x = − 1 2 , y = 1 2 − 3 y + z = 0 , z = 3 2 T = c ρ r 3 s ⇒ ΔT T = 1 2 Δρ ρ + 3 2 Δr r + 1 2 Δs s = 1 2 + 3 + 1 2 = 4

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