If pressure at half of depth of a lake is equal to the (1/4) pressure at the bottom of the lake then what is the depth of the lake?

Question

If pressure at half of depth of a lake is equal to the (1/4) pressure at the bottom of the lake then what is the depth of the lake? (A) 30.6 m (B) 41.6 m (C) 53.4 m (D) 56 m

Tardigrade Admin · Accepted Answer

Pressure at the bottom = P o + h ρ g Pressure at half the depth = P o +( h /2) ρ g ∴ P0+(h/2) ρ g=(1/4)(P0+h ρ g) 4 P0+4 (h/2) ρ g=P0+h ρ g 4 P0+2 h ρ g=P0+h ρ g ⇒ 3 P0=-h ρ g ⇒ (-3 P0/ρ g)=h h =-((3 × 105/103 × 9.8)) =-0.306 × 102=-30.6 m (-ve sign indicates depth but only magnitude is considerd)

Q. If pressure at half of depth of a lake is equal to the $\frac{1}{4}$ pressure at the bottom of the lake then what is the depth of the lake?

$30.6 m$

$41.6 m$

$53.4 m$

$56 m$

Q. If pressure at half of depth of a lake is equal to the 41​ pressure at the bottom of the lake then what is the depth of the lake?

30.6m

41.6m

53.4m

56m

Q. If pressure at half of depth of a lake is equal to the $\frac{1}{4}$ pressure at the bottom of the lake then what is the depth of the lake?

$30.6 m$

$41.6 m$

$53.4 m$

$56 m$