NEETPhysicsMechanical Properties of Solids
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The compressibility of a material is always a positive quantity. Reason (R): In the mathematical expression for compressibility, k = - 1 P ( V V ) , the negative sign accounts for the fact that an increase in pressure results in a decrease in volume. In the light of the above statements, choose the
Options
- ABoth (A) and (R) are correct and (R) is the correct explanation of (A)
- BBoth (A) and (R) are correct but (R) is not the correct explanation of (A)
- C(A) is correct but (R) is not correct
- D(A) is not correct but (R) is correct
Correct answer
A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
Step-by-step solution
Compressibility is defined as the reciprocal of the bulk modulus of a material. For any stable material, a positive increase in pressure ( P > 0 ) leads to a decrease in volume ( V To ensure that the bulk modulus and its reciprocal (compressibility) are positive physical quantities, a negative sign is explicitly included in their defining formulas. Thus, k = - 1 P ( V V ) yields a positive value because the negative V cancels with the negative sign in the formula. Therefore, both Assertion and Reason are correct, a