Question

9. A sphere contracts in volume by 0.01% when taken
to the bottom of sea 1 km deep. Find Bulk
modulus of the material of sphere
(1) 9.8 x 106 N/m (2) 1.2 x 1010 N/m2
(3) 9.8 x 1010 N/
m2 (4) 9.8 x 10 N/m

Answer 1

Correct option is

C9.8×1010N/M2

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 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

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