A bubble is at the bottom of the lake of depth h . As the bubble comes to surface, its radius increases three times. If atmospheric pressure is equal to l metre of water column, then h is equal to

Question

A bubble is at the bottom of the lake of depth h . As the bubble comes to surface, its radius increases three times. If atmospheric pressure is equal to l metre of water column, then h is equal to (A) 26 l (B) l (C) 25 l (D) 30 l

Tardigrade Admin · Accepted Answer

From Boyle's law pV= constant ∴ p1V1=p2V2 Here, p1=ρ g(h + l), V1=(4/3)π r3 p2=ρ g l, V2=(4/3) π(3 r)3 ∴ (h + l)(4/3)π r3=l× (4/3)π (3 r)3 or h+l=27l ∴ h=26l <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-tf9ljnxucoma.png" />

Q. A bubble is at the bottom of the lake of depth $h$ . As the bubble comes to surface, its radius increases three times. If atmospheric pressure is equal to $l$ metre of water column, then $h$ is equal to

$26 l$

$l$

$25 l$

$30 l$

From Boyle's law
$p V =$ constant
$∴ p_{1} V_{1} = p_{2} V_{2}$
Here, $p_{1} = ρ g (h + l), V_{1} = \frac{4}{3} π r^{3}$
$p_{2} = ρ g l, V_{2} = \frac{4}{3} π (3 r)^{3}$
$∴ (h + l) \frac{4}{3} π r^{3} = l \times \frac{4}{3} π (3 r)^{3}$
or $h + l = 27 l$
$∴ h = 26 l$

Q. A bubble is at the bottom of the lake of depth h . As the bubble comes to surface, its radius increases three times. If atmospheric pressure is equal to l metre of water column, then h is equal to

26l

l

25l

30l

From Boyle's law pV= constant ∴p1​V1​=p2​V2​ Here, p1​=ρg(h+l),V1​=34​πr3 p2​=ρgl,V2​=34​π(3r)3 ∴(h+l)34​πr3=l×34​π(3r)3 or h+l=27l ∴h=26l

Q. A bubble is at the bottom of the lake of depth $h$ . As the bubble comes to surface, its radius increases three times. If atmospheric pressure is equal to $l$ metre of water column, then $h$ is equal to

$26 l$

$l$

$25 l$

$30 l$

From Boyle's law
$p V =$ constant
$∴ p_{1} V_{1} = p_{2} V_{2}$
Here, $p_{1} = ρ g (h + l), V_{1} = \frac{4}{3} π r^{3}$
$p_{2} = ρ g l, V_{2} = \frac{4}{3} π (3 r)^{3}$
$∴ (h + l) \frac{4}{3} π r^{3} = l \times \frac{4}{3} π (3 r)^{3}$
or $h + l = 27 l$
$∴ h = 26 l$