Question 310: Properties of Matter

Question

A soap bubble of radius 3 cm is formed inside the another soap bubble of radius 6 cm. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is ................ cm.

Accepted Answer

Image
Excess pressure inside the smaller soap bubble
$$\Delta P = {{4S} \over {{r_1}}} + {{4S} \over {{r_2}}}$$ .... (i)
The excess pressure inside equivalent soap bubble
$$\Delta P = {{4S} \over {{R_{eq}}}}$$ ....... (ii)
From (i) & (ii)
$${{4S} \over {{R_{eq}}}} = {{4S} \over {{r_1}}} + {{4S} \over {{r_2}}}$$
$${1 \over {{R_{eq}}}} = {1 \over {{r_1}}} + {1 \over {{r_2}}}$$
$$ = {1 \over 6} + {1 \over 3}$$
R
eq
= 2 cm

Properties of Matter

A soap bubble of radius 3 cm is formed inside the another soap bubble of radius 6 cm. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is ................ cm.

Integer / Numeric Answer Type