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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

  1. ABoth (A) and (R) are correct and (R) is the correct explanation of (A)
  2. BBoth (A) and (R) are correct but (R) is not the correct explanation of (A)
  3. C(A) is correct but (R) is not correct
  4. 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

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