Question

The pressure acting on a submarine is 3 × 10⁵ Pa at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be ______.

(Assume that atmospheric pressure is 1 × 10⁵ Pa density of water is 10³ kg m^–3, g = 10 ms^–2)

Options

• `200/3%`

• `5/200%`

• `200/5%`

• `3/200%`

Answer 1

The pressure acting on a submarine is 3 × 10⁵ Pa at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be `bb(200/3%)`.

Explanation:

According to Hydrostatic's Law

P = P₀ + hρg

Given,

P₁ = 3 × 10⁵Pa

So, P₁ = P₀ + hρg

hρg = [3 × 10⁵ - 10⁵] Pa = 2 × 10⁵Pa

If depth is doubled.

2hρg = 2 × 2 × 10⁵ ⇒ 4 × 10⁵ Pa

So, P₂ = P₀ + 4 × 10⁵ ⇒ 5 × 10⁵Pa

% increase in pressure

= `("P"_2-"P"_1)/"P"_1xx100`

= `((2xx10^5)/(3xx10^5))xx100`

= `200/3`%