Assertion : A given mass of a gas is subjected to an external pressure of `0.5xx10^(10) N//m^(2)` , the bulk modulus of the gas is `0.5xx10^(10) N//m^(2)` . The ratio of the density of the gas before and after applying the external pressure is `1 : 1`
Reason : Pressure is inversely proportional to density of gas and bulk modulus is inversely proportional to change in volume

Options

A. both Assertion and Reason are true and the Reason in the correct explanation of the Assertion.
B. both Assertion and Reason are true but Reason is not a correct explanation of the Assertion.
C. Assertion is true but the Reason is false.
D. both Assertion and Reason are false.

Answer

D

Explanation

Density, `rho = (M)/(V)` , Taking log and differentiating it, we have `(d rho)/(rho) = - (dV)/(V)`
Bulk modulus, `K = -(d P)/(Delta V//V) = (0.5xx10^(10))/((Delta rho//rho))` or `(Delta rho)/(rho) = (0.5xx10^(10))/(0.5xx10^(10)) =1` or `Delta rho = rho`
`:. rho' = rho + d rho =rho + rho = 2 rho`
Hence `rho//rho' =1//2`
Thus Assertion is wrong and Reason is wrong.