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.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
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).
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Strain is a dimensionless quantity.
Reason R: Unit of Young’s modulus is same as that of stress.
In the light of the above statements, choose the correct answer from the option given below.
1. Both A and R are true and R is the correct explanation of A
2. Both A and R are true but R is not the correct explanation of A
3. A is true but R is false
4. A is false but R is true
View Answer
Strain is indeed dimensionless since it's the ratio of two similar physical quantities (change in dimension over original dimension). The unit of Young's modulus is indeed identical to stress (both are \(\text{N/m}^2\)). However, the second statement is not the reason for the first.