Question
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
BITSAT
Physics
Units and Dimensions
2023
BITSAT 2023 (Memory Based Paper 2)
BITSAT Physics Question (2023) — Solution
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 )
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
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