Question

Assertion :The stress-strain graphs are shown in the figure for two materials $A$ and $B$ are shown in figure. Young's modulus of $A$ is greater than that of $B$. Reason: The Young's modules for small strain is, $Y=\frac{stress}{strain}$ = slope of linear portion of graph; and slope of $A$ is more than that of $B$.

• A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
• B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
• C. STATEMENT-1 is True, STATEMENT-2 is False
• D. STATEMENT-1 is False, STATEMENT-2 is True

Answer 1

The correct option is A STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

Lets see the reason statement first:

Young's modulus is indeed defined as

$Y=\frac{stress}{strain}$

Slope of the graph shown will be

$\frac{dy}{dx}=\frac{stress}{strain}$

Combining the two statements we get:

$Y=\frac{stress}{strain}$

Observing the graph it is clearly visible that slope of $A$ is more than slope of $B$

Thus reason statement is completely correct.

Coming to the Assertion statement, from Reason statement we know that $Y=slope$ $of$ $linear$ $portion$.

Since slope of A is more than slope of B, it follows that Young's modulus of A is greater than that of B.

Thus Assertion is also correct.