When a large bubble rises from the bottom of a lake to the surface, its radius triples. If atmospheric pressure is equal to that of column of water height H, then the depth of the lake (h) is

Question

When a large bubble rises from the bottom of a lake to the surface, its radius triples. If atmospheric pressure is equal to that of column of water height H, then the depth of the lake (h) is (A) 28 H (B) 25 H (C) 27 H (D) 26 H

Tardigrade Admin · Accepted Answer

According to the relation, P 1 V 1= P 2 V 2 ( H + h ) ρ g × (4/3) π r 3= H ρ g × (4/3) π(3 r )3 ( H + h ) r 3=27 Hr 3 ⇒ h =26 H

Q. When a large bubble rises from the bottom of a lake to the surface, its radius triples. If atmospheric pressure is equal to that of column of water height $H$ , then the depth of the lake (h) is

$28 H$

$25 H$

$27 H$

$26 H$

According to the relation, $P_{1} V_{1} = P_{2} V_{2}$
$(H + h) ρ g \times \frac{4}{3} π r^{3} = H ρ g \times \frac{4}{3} π (3 r)^{3}$
$(H + h) r^{3} = 27 H r^{3}$
$\Rightarrow h = 26 H$

Q. When a large bubble rises from the bottom of a lake to the surface, its radius triples. If atmospheric pressure is equal to that of column of water height H, then the depth of the lake (h) is

28H

25H

27H

26H