Question

If pressure at half the depth of a lake is equal to 2/3 pressure at the bottom of the lake then what is the depth of the lake

• A. 10m
• B. 20m
• C. 60m
• D. 30m

Answer 1

Answer: (B)

20m

Answer 2

Pressure at half the depth $= P _ { 0 } + \frac { h } { 2 } d g$

Pressure at the bottom $= P _ { 0 } + h d g$

According to given condition

$P _ { 0 } + \frac { h } { 2 } d g = \frac { 2 } { 3 } \left( P _ { 0 } + h d g \right)$

⇒$3 P _ { 0 } + \frac { 3 h } { 2 } d g = 2 P _ { 0 } + 2 h d g$

$\Rightarrow h = \frac { 2 P _ { 0 } } { d g } = \frac { 2 \times 10 ^ { 5 } } { 10 ^ { 3 } \times 10 } = 20 \mathrm {~m}$