Question

19. The atmospheric pressure at a given place equals P. The radii of two
bubbles, blown from a given soap solution of surface tension T, are 2R
and R respectively. The ratio of pressure inside them equals:
2PR + 41
2PR + 8T
PR + 2T
PR + 8T
PV + R/2
PT +2R
T +4P/R
(4) TARP​

Answer 1

A )   { 4T +2PR) / 2PR+8T } WILL BE The ratio of pressure inside them .

Explanation:

P i - P o = $\frac{4T}{radius }$

now for sopa bubble 1

P i₁- P  = 4T/2R  ........eq 1

now for sopa bubble 2

P i₂ - P  = 4T / R ........ equation 1 from 2

From eq 2

4T/R = P i₂ - P

using above in eq 1 we get

P i₁- P  = (P i₂ - P )/2

2 (P i₁- P ) = (P i₂ - P )

2P i₁- 2 P  = (P i₂ - P )

2P i₁ = (P i₂ + P )

dividing by P i ₂  we get

2 (P i₁ / P i ₂ ) = 1 + (P / P i ₂ ) ............................eq 3

putting the value of P i ₂ from eq 2

P i₂ =  P  +  4T / R

P i₂ =  P  +  4T / R

P / P i₂ = P R / (PR+4T)

using above in eq 3

2 (P i₁ / P i ₂ ) = 1 + P R / (PR+4T)

                      = (4T +2PR) / 2PR+8T )