Question

Assertion: When a solid iron ball is heated, the percentage increase is its largest volume is largest.
Reason: Coefficient of superficial expansion is twice that of linear expansion whereas coefficient of volume expansion is three times of linear expansion.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect

Answer 1

Hint:To answer this question, we first need to know the value of coefficient of volume expansion which is $\gamma = 3\alpha $ and $\gamma = 1.5\beta $ which is 3 times the linear expansion and 1.5 times the areal expansion.

Complete answer:
As discussed above about the values of coefficient of volume expansion where we can clearly see that the coefficient of volumetric expansion is maximum as compared to both linear or areal expansion. So it's clear that on expansion the volume expansion will be more as comparison to expansion of both area and linear. Therefore, the percentage increase in volume is maximum.So, assertion is correct.

Also as seen in the hint about values of coefficients proves that Reason is also correct.As explained in the hint also the value of volume expansion is 1.5 times area expansion and 3 times that of linear expansion.So , the reason is also correct. And also, the reason properly explains the situation in assertion. As this given reason is the correct explanation for the assertion i.e. of maximum increase in volumetric expansion. So, reason properly explains the assertion.

Hence, the correct answer is option A.

Note: The coefficient of thermal expansion explains how an object's size increases as the temperature changes. It calculates the fractional change in size per degree change in temperature at constant strain, with lower coefficients indicating a lower tendency for size change.