Question

A solid sphere of radius R when taken to a depth of 100 m in water gets compressed so that its radius decreases by 0.1%. The value of bulk modulus of the material of the sphere is

(density of water = 10³ kg m^-3; g = 10ms^-2)

(1) 10⁵ Nm^-2

(2) 1/3 x 10⁹ Nm^-2

(3) 10⁹ NM^-2

(4) 4/3 x 10⁹ NM^-2

Answer 1

(2) 1/3 x 10⁹ Nm^-2

The pressure due to liquid column at 100 m depth = hpg = 10² x 10³ x 10 Nm^-2 Let V be volume of sphere on surface of earth. Obviously

V = 4/3 πR³

Let (V - ΔV) be the volume of sphere at a depth of 100 m. Then