A liquid of bulk modulus k is compressed by applying an external pressure such that its density increases by 0.01 %. The pressure applied on the liquid is

Question

A liquid of bulk modulus k is compressed by applying an external pressure such that its density increases by 0.01 %. The pressure applied on the liquid is (A) (k/10000) (B) (k/1000) (C) 1000 k (D) 0.01 k

Tardigrade Admin · Accepted Answer

k = (P/Δ v/v ) ⇒ (P/k) = (Δ V/V) = (Δρ/ρ) ⇒ P = (kΔρ/ρ) = (k/1000)

Q. A liquid of bulk modulus $k$ is compressed by applying an external pressure such that its density increases by $0.01%$ . The pressure applied on the liquid is

$\frac{k}{10000}$

$\frac{k}{1000}$

1000 k

0.01 k

$k = \frac{P}{Δ v / v} \Rightarrow \frac{P}{k} = \frac{Δ V}{V} = \frac{Δ ρ}{ρ}$
$\Rightarrow P = \frac{k Δ ρ}{ρ} = \frac{k}{1000}$

Q. A liquid of bulk modulus k is compressed by applying an external pressure such that its density increases by 0.01%. The pressure applied on the liquid is

10000k​

1000k​