Question 188: Properties of Matter

Question

A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let P
2
be the pressure inside the inner bubble and P
0
, the pressure outside the outer bubble. Radius of another bubble with pressure difference P
2
$$-$$ P
0
between its inside and outside would be :

Accepted Answer

Pressure difference inside the inner  bubble,
p
2
$$-$$ p
1
= $${{4T} \over {{r_2}}}$$b . . . . . (1)
And for outer bubble
p
1
$$-$$ p
0
= $${{4T} \over {{r_1}}}$$ . . . . . . . (2)
$$	herefore\,\,\,$$ p
2
$$-$$ p
0
= 4T $$\left( {{1 \over {{r_2}}} + {1 \over {{r_1}}}} ight)$$
$$ \Rightarrow $$$$\,\,\,$$ p
2
$$-$$ p
0
= $${{4T} \over r}$$
Here r is the radius of the bubble.
$$	herefore\,\,\,$$ $${1 \over r} = {1 \over {{r_2}}} + {1 \over {{r_1}}}$$
$$ \Rightarrow $$$$\,\,\,$$ r = $${{{r_1}{r_2}} \over {{r_1} + {r_2}}}$$
= $${{4 	imes 6} \over {4 + 60}}$$
= 2.4 cm

Answer

12 cm

Answer

2.4 cm

Answer

6 cm

Answer

4.8 cm

Properties of Matter

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