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The bulk modulus of elasticity of the ma...

The bulk modulus of elasticity of the material of a metal sphere is `2 xx 10^(11) N//m^(2)`. In open air, atmospheric pressure of `10^(5) N//m^(2)` acts on it. What is the fractional change in its volume if it is kept in a vacuum chamber ?

A

`2 xx 10^(-7)`

B

`3 xx 10^(-7)`

C

`4 xx 10^(-7)`

D

`5 xx 10^(-7)`

Text Solution

Verified by Experts

The correct Answer is:
D
Bulk modulus K `= (V dP)/(dV)`
`:. K dV = V dP` or `(dV)/(V) = (dP)/(K)`
In open air, the atmospheric pressure acts on it.
In vacuum, the pressure is reduced from `10^(5) N//m^(2)` to zero.
`:. dP = 10^(5) N//m^(2)` as a result, there is a slight increase in its volume
and `(dV)/(V) = (dP)/(K) = (10^(5))/(2 xx 10^(11)) = 5 xx 10^(-7)`
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