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

Short Solution (Best for NEET):

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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