Elasticity and Work Done in Springs – Rankers Physics

Solids: Practice Problem & Solution

Assertion (A): Identical springs of steel and copper are equally stretched. More work will be done on the steel spring. Reason (R): Steel is more elastic than copper.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Solids. Understanding the underlying formula is key to arriving at the correct answer below:

Assertion (A) is true. Work done to stretch a spring is \(W = \frac{1}{2} k x^2\). Steel has a higher Young's modulus than copper, implying a higher spring constant \(k\) for identical dimensions.

Thus, more work is done on the steel spring.

Reason (R) is true. Steel is indeed more elastic than copper (possesses a higher Young's modulus).

Reason (R) correctly explains Assertion (A).

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1. A wire of length $L$ area of cross section $A$ is hanging from a fixed support. The length of the wire changes to $L_1$ when mass $M$ is suspended from its free end. The expression for Young's modulus is: (2020)
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