Question

A sphere contracts in volume by 0.005% when it is taken to the bottom of sea of 2.5 km . What is the bulk modulus and compressibility of the sphere​

Answer 1

Answer:

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 of sphere is V

So, dV=0.01% of V

Now,

dV=

100

0.01V

V

dV

=

100

0.01

V

dV

=10

−4

Now, the change in pressure

dP=ρg(dh)

dP=10

3

×9.8×10

3

dP=9.8×10

6

N/m

2

Now, the bulk modulus is

K=

V

dV

dP

K=

10

−4

9.8×10

6

K=9.8×10

10

N/m

2

Hence, the bulk modulus of the material of sphere is 9.8×10

10

N/m

2