Question

A spherical body contract in volume by 0.1% when taken to 500 m deep in the sea. find the bulk modulus of he material of the body?​

Answer 1

Answer:

Given that, Sphere contracts in volume 0.01 Change in Depth = 1 km Acceleration due to gravity = 9.8 m/s2 Density of water = 1000 kg/m3 Now, the volume

Explanation:

Answer 2

Given,

Volume contraction by 0.1%

Depth of the sea = 500m

To find,

The bulk modulus of the material of the body

Solution,

The bulk modulus of the material of the body is 4.9*10⁹ N/m².

We can simply solve the numerical problem by the following procedure.

We know that,

Sphere contracts in volume 0.1%

Depth = 500m

g = 9.8 m/s²

Density of water = 1000 kg/m³

Now,

Let the volume of the sphere be V.

∴ dV = 0.1% of V

⇒ $\frac{dV}{V} = \frac{0.1}{100}$

        = 0.001

        = 10⁻³

Now,

Change in the pressure = ρ g (dh)

                                        = 1000 * 9.8 * 500

                                        = 4.9 x 10⁶ N/m²

Now,

∴ Bulk Modulus = $\frac{dP}{\frac{dV}{V} }$

                          = $\frac{4.9*10^{6}}{10^{-3}}$

                          = 4.9 * 10⁹ N/m²

Thus,

The bulk modulus of the material of the body is 4.9*10⁹ N/m².