NEET2025PhysicsUnits and DimensionsActual
A balloon is made of a material of surface tension S and its inflation outlet (from where gas is filled in it) has small area A . It is filled with a gas of density and takes a spherical shape of radius R . When the gas is allowed to flow freely out of it, its radius changes from R to 0 (zero) in time T . If the speed (r) of gas coming out of the balloon depends on r as r^ and T S^ A^ ^ R^ then
Options
- Aa= 1 2 , = 1 2 , =-1, =+1, = 3 2
- Ba=- 1 2 , =- 1 2 , =-1, =- 1 2 , = 5 2
- Ca=- 1 2 , =- 1 2 , =-1, = 1 2 , = 7 2
- Da= 1 2 , = 1 2 , =- 1 2 , = 1 2 , = 7 2
Correct answer
C. a=- 1 2 , =- 1 2 , =-1, = 1 2 , = 7 2
Step-by-step solution
aligned & T Time [ T ^1 ] & S Surface Tension S = F = [ M ^1 ~L ^1 ~T ⁻² ] [ L ^1 ] = [ M ^1 ~T ⁻² ] & A Area [ L ^2 ] & density [ M ^1 ~L ⁻³ ] & R Radius [ L ^1 ] & With Dimensional Analysis & T S ^ A ^ ^ R ^ & [ M ^0 ~L ^0 ~T ^1 ]= [ MT ⁻² ]^ [ L ^2 ]^ [ ML ⁻³ ~V ^ [ L ]^ . & [ M ^0 ~L ^0 ~T ^1 ]= [ M ^ + , L ^ 2 + -3 , ~T ^ -2 ] & -2 =1 & =- 1 2 & + =0 & 2 + -3 =0 & 2 + -3 ( 1 2 )=0 & 2 + = 3 2 aligned