Question

A spherical ball contracts in volume by 0.01%
when subjected to a normal uniform pressure of
100 atm. The Bulk modulus of its material is​

Answer 1

Answer:

Given:

A spherical ball contracts in volume by 0.01% . Pressure experienced is 100 atm.

To find:

Bulk modulus of elasticity.

Definitions:

Bulk modulus of elasticity is defined as the ratio of volumetric stress and volumetric strain.

The volumetric stress is the excess pressure, and the volumetric strain is the volume change wrt to initial volume.

so , volumetric stress = ∆P,

Volumetric strain = (∆V/V)

Calculation:

Bulk modulus is denoted by "K".

So, K = ∆P/(∆V/V)

=> K = 100/(0.01%)

=> K = 100/(0.01/100)

=> K = 10^6 atm.

Conversation:

1 atm = 10^5 Pascal.

So converting Bulk modulus to SI unit

K = 10 ^(5+6) = 10^ 11 Pascal.

So the answer is 10^11 Pascal.

Answer 2

Question :-

A spherical ball contracts in volume by 0.01% .when subjected to a normal uniform pressure of 100 atm. The Bulk modulus of its material is ..?

Answer :-

$\boxed{ \sf{b \: = {10}^{11} \: \: \frac{N}{ {m}^{2} } }} \:$

To find :-

→ Bulk modulus

Formula used :-

$\implies \: \sf{B \: = \frac{\Delta\:P}{ \frac{\Delta \:v}{v} }}$

Step - by - step explanation :-

Given that ,

• Pressure (P) = 100 ATM

• Volume contracts is 0.01%

Now

applying the given formula ,for bulk modulus (B)

$\rightarrow \red{\sf{B \: = \frac{100 \times {10}^{5} }{ \frac{0.01}{100} } }} \\ \\ \rightarrow \green{\sf{B \: = \frac{ {10}^{7} \times {10}^{2} }{0.01} }} \\ \\ \rightarrow \sf{ B \: = {10}^{9 + 2} } \\ \\ \rightarrow \boxed{ \red{ \sf{B \: = {10}^{11} }\: \: \frac{N}{ {m}^{2} } }} \\ \\ \red{\sf{bulk \: modulus \: is \: } \green{ {10}^{11} \: \: \frac{N}{ {m}^{2} } }}$

______________________________