Bulk modulus for rubber is 9.8 × 108 Nm -2. To what depth (in m ) should a rubber ball be taken in a lake so that its volume is decreased by 0.1 % ?

Question

Bulk modulus for rubber is 9.8 × 108 Nm -2. To what depth (in m ) should a rubber ball be taken in a lake so that its volume is decreased by 0.1 % ? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

K=((Δ P) V/Δ V) text or Δ P=(K Δ V/V) Let h be the required depth and the density of water be ρ. Then h ρ g=(K Δ V/V) or h=(K Δ V/ρ g V)=(9.8 × 108 × 0.1/103 × 9.8 × 100) =100 m

Q. Bulk modulus for rubber is $9.8 \times 1 0^{8} N m^{- 2}$ . To what depth (in $m$ ) should a rubber ball be taken in a lake so that its volume is decreased by $0.1%$ ?

$K = \frac{( Δ P ) V}{Δ V} or Δ P = \frac{K Δ V}{V}$
Let $h$ be the required depth and the density of water be $ρ$ .
Then $h ρ g = \frac{K Δ V}{V}$
or $h = \frac{K Δ V}{ρ g V} = \frac{9.8 \times 1 0 ^{8} \times 0.1}{1 0 ^{3} \times 9.8 \times 100}$
$= 100 m$

Q. Bulk modulus for rubber is 9.8×108Nm−2. To what depth (in m ) should a rubber ball be taken in a lake so that its volume is decreased by 0.1% ?

K=ΔV(ΔP)V​ or ΔP=VKΔV​ Let h be the required depth and the density of water be ρ. Then hρg=VKΔV​ or h=ρgVKΔV​=103×9.8×1009.8×108×0.1​ =100m

Q. Bulk modulus for rubber is $9.8 \times 1 0^{8} N m^{- 2}$ . To what depth (in $m$ ) should a rubber ball be taken in a lake so that its volume is decreased by $0.1%$ ?

$K = \frac{( Δ P ) V}{Δ V} or Δ P = \frac{K Δ V}{V}$
Let $h$ be the required depth and the density of water be $ρ$ .
Then $h ρ g = \frac{K Δ V}{V}$
or $h = \frac{K Δ V}{ρ g V} = \frac{9.8 \times 1 0 ^{8} \times 0.1}{1 0 ^{3} \times 9.8 \times 100}$
$= 100 m$