Question

A sphere contracts in volume by 0.01% when taken to the bottom of sea 1 km deep. If the density of sea water is 10^3 kg m^−3 , find the bulk modulus of the material of the sphere.

Answer 1

Let the volume of sphere is V
Now , sphere contracts in volume 0.01%
Means dV = 0.01% of V = 0.01V/100
so, dV/V = 0.01V/100V = 0.01/100 = 10⁻⁴

Now, dP = ρg(dh)
Here ρ is density of water , g is acceleration due to gravity and dh is change in depth .Here, ρ = 10³ kg/m³ , g = 9.8m/s² and dh = 1 km
∴dP = 10³ × 9.8 × 10³ = 9.8 × 10⁶ N/m²

Now, bulk modulus , k = dP/dV/V
= 9.8 × 10⁶/10⁻⁴ = 9.8 × 10¹⁰ N/m²

Answer 2

Formula of Bulk Modulus= P/∆v/v

=density×g×h/0.01/100

=1000×9.8×1000/1/1000

=9.8×10^10