When a sphere is taken to bottom of sea 1 km deep, it contracts by 0.01%. The bulk modulus of elasticity of the material of sphere is (Given, density of water = 1 gcm-3)

Question

When a sphere is taken to bottom of sea 1 km deep, it contracts by 0.01%. The bulk modulus of elasticity of the material of sphere is (Given, density of water = 1 gcm-3) (A) 9.8×1010Nm-2 (B) 10.2×1010Nm-2 (C) 0.98×1010Nm-2 (D) 8.4×1010Nm-2

Tardigrade Admin · Accepted Answer

Bulk modulus B=(Δ p/(-Δ V)V) (-Δ V/V)=(0.01/100)=10-4 Δ p=pressure of water=hρ g = 103×1×10×9.8 Δ p=9.8×106 B=(9.8×106/10-4) =9.8×1010Nm-2

Q. When a sphere is taken to bottom of sea 1 km deep, it contracts by 0.01%. The bulk modulus of elasticity of the material of sphere is (Given, density of water $= 1 g c m^{- 3})$

$9.8 \times 1 0^{10} N m^{- 2}$

$10.2 \times 1 0^{10} N m^{- 2}$

$0.98 \times 1 0^{10} N m^{- 2}$

$8.4 \times 1 0^{10} N m^{- 2}$

Bulk modulus $B = \frac{Δ p}{\frac{- Δ V}{V}}$
$\frac{- Δ V}{V} = \frac{0.01}{100} = 1 0^{- 4}$
$Δ p = p ress u reo f w a t er = h ρ g$
= $1 0^{3} \times 1 \times 1 0^{\times} 9.8$
$Δ p = 9.8 \times 1 0^{6}$
$B = \frac{9.8 \times 1 0 ^{6}}{1 0 ^{- 4}}$
$= 9.8 \times 1 0^{10} N m^{- 2}$

Q. When a sphere is taken to bottom of sea 1 km deep, it contracts by 0.01%. The bulk modulus of elasticity of the material of sphere is (Given, density of water =1gcm−3)

9.8×1010Nm−2

10.2×1010Nm−2

0.98×1010Nm−2

8.4×1010Nm−2