Question

A soap bubble of radius 2.0 cm is formed inside another soap bubble of radius 4.0 cm. The radius of another soap bubble which has the same pressure difference as that between the inside of the smaller and outside of large soap bubble, in metres is ______

Options

• 1.3 x 10^-2

• 3.3 x 10^-2

• 2.2 x 10^-2

• 4.5 x 10^-2

Answer 1

1.3 x 10^-2

Explanation:

ΔP₁ = pressure difference between a smaller bubble and larger bubble

ΔP₂ = pressure difference between inside and outside the larger bubble

Now, ΔP₁ = `(4"T")/"R"_1`, ΔP₂ = `(4"T")/"R"_2`

As required pressure difference ΔP = `(4"T")/"R"`

ΔP = ΔP₁ + ΔP₂ 

∴ `(4"T")/"R" = (4"T")/("R"_1) + (4"T")/("R"_2)`

R = `("R"_1"R"_2)/("R"_1 + "R"_2) = (2 xx 4 xx 10^-4)/((2 + 4) xx 10^-2) = 1.3 xx 10^-2`m