When a sphere is taken to bottom of sea 1 km deep, it contracts by 0.01 %. The bulk modulus of

step 1 In this problem, let V be the volume of sphere. So I can write the value of dv is equal to 0 .01

When a sphere is taken to bottom of sea 1 km deep, it...

When a sphere is taken to bottom of sea $1 \mathrm{~km}$ deep, it contracts by $0.01 \%$. The bulk modulus of elasticity of the material of sphere is: (Given: Density of water $\left.=1 \mathrm{~g} / \mathrm{cm}^{3}\right)$ (a) $9.8 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$ (b) $10.2 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$ (c) $0.98 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$ (d) $8.4 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$

When a sphere is taken to bottom of sea $1 \mathrm{~km}$ deep, it contracts by $0.01 \%$. The bulk modulus of elasticity of the material of sphere is: (Given: Density of water $\left.=1 \mathrm{~g} / \mathrm{cm}^{3}\right)$
(a) $9.8 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
(b) $10.2 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
(c) $0.98 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
(d) $8.4 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$

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Key Concepts

Volume Compression

Volume compression in this context describes the fractional decrease in an object's volume when subjected to an external pressure. It is expressed as the ratio of change in volume (?V) to the original volume (V). This measurement, when combined with the applied pressure, allows one to determine the bulk modulus and assess the material's compressibility.

Bulk Modulus of Elasticity

This is a measure of a material's resistance to uniform compression under applied pressure. It is defined as the ratio of the applied pressure to the relative volume change, mathematically expressed as B = -P/(?V/V). This concept is fundamental in understanding how materials behave under high-pressure conditions.

Hydrostatic Pressure

Hydrostatic pressure refers to the pressure exerted by a fluid at a given depth as a result of the weight of the fluid above. It is calculated using the formula P = ?gh, where ? is the density of the fluid, g is the acceleration due to gravity, and h is the depth. This concept is essential in problems involving objects submerged in fluids.

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