Assertion (A): The coefficient of volume expansion of a solid is approximately three times its coefficient of linear expansion. Reason (R): Volume is a three-dimensional property derived from cubing the linear dimension. MCQ with Answer and Explanation

Assertion (A): The coefficient of volume expansion of a solid is approximately three times its coefficient of linear expansion. Reason (R): Volume is a three-dimensional property derived from cubing the linear dimension.
A. Both A and R are true and R is the correct explanation of A.
B. Both A and R are true but R is NOT the correct explanation of A.
C. A is false but R is true.
D. A is true but R is false.
Answer: Option A
Solution (By JKExamLibrary)
The coefficient of linear expansion is alpha. A cube of side L has volume V = L^3. When heated, the new length is L(1+alphadT). The new volume is [L(1+alphadT)]^3. Expanding via binomial theorem and ignoring higher-order small terms gives V' = V(1 + 3alphadT). Thus, the volume expansion coefficient gamma is equal to 3alpha. Reason R correctly explains Assertion A.

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