The frequency ( v ) of an oscillating liquid drop may depend upon radius ( r ) of the drop, density ( ρ ) of liquid and the surface tension ( s ) of the liquid as : v = r a ρ b s c . The values of a ,

Question

The frequency ( v ) of an oscillating liquid drop may depend upon radius ( r ) of the drop, density ( ρ ) of liquid and the surface tension ( s ) of the liquid as : v = r a ρ b s c . The values of a , b and c respectively are

TestHub · Accepted Answer

​ v = r a ρ b s c ⇒ [ v ] = [ r ] a [ ρ ] b [ s ] c ⇒ [ T − 1 ] = [ L 1 ] a [ M 1 L − 3 ] b [ L MLT ​ ] − 2 ⇒ T − 1 = M b + c ⋅ L a − 3 b ⋅ T − 2 c ⇒ b + c = 0 , a − 3 b = 0 , − 2 c = − 1 ⇒ c = 2 1 ​ , b = − 2 1 ​ , a − 3 b = 0 ; a + 2 3 ​ = 0 ⇒ a = − 2 3 ​ ​

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