NEET
- Exam
- NEET
- Subject
- Physics
- Chapter
- Mechanical Properties of Solids
NEET · Physics · Mechanical Properties of Solids
Given below are two statements: one is labelled as Assertion (A)...
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, , 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 most appropriate answer from the options given below:
Assertion (A): The compressibility of a material is always a positive quantity.
Reason (R): In the mathematical expression for compressibility, , 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 most appropriate answer from the options given below:
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 () leads to a decrease in volume ().
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, \left(\dfrac{\Delta V}{V}\right)\Delta V cancels with the negative sign in the formula.
Therefore, both Assertion and Reason are correct, and the Reason correctly explains the Assertion.
Answer: Both (A) and (R) are correct and (R) is the correct explanation of (A)
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, \left(\dfrac{\Delta V}{V}\right)\Delta V cancels with the negative sign in the formula.
Therefore, both Assertion and Reason are correct, and the Reason correctly explains the Assertion.
Answer: Both (A) and (R) are correct and (R) is the correct explanation of (A)