BITSAT2023PhysicsUnits and DimensionsActual
The frequency (v) of an oscillating liquid drop may depend upon radius (r) of the drop, density ( ) of liquid and the surface tension (s) of the liquid as : v=r^a ^b s^c . The values of a, b and c respectively are
Options
- A(- 3 2 ,- 1 2 ; 1 2 )
- B( 3 2 ,- 1 2 , 1 2 )
- C( 3 2 , 1 2 ;- 1 2 )
- D(- 3 2 , 1 2 , 1 2 )
Correct answer
A. (- 3 2 ,- 1 2 ; 1 2 )
Step-by-step solution
aligned & v= r ^ a ^ b s ^ c [v]=[ r ]^ a [ ]^ b [ s ]^ c & [ T ⁻¹ ]= [ L ^1 ]^ a [ M ^1 ~L ⁻³ ]^ b [ MLT L ]⁻² & T ⁻¹= M ^ b + c L ^ a -3 ~b T ^ -2 c & b + c =0, a -3 ~b =0,-2 c =-1 & c = 1 2 , ~b =- 1 2 , a -3 ~b =0 ; & a + 3 2 =0 a =- 3 2 aligned