A composite rod consists of a steel rod of length `25 cm` and area `2A` and a copper rod of length `50 cm` and area `A`. The composite rod is subjected to an axial load `F`. If the Young's moduli of steel and copper are in the ratio `2: 1` then

Options

A. the extension produced in copper rod will be more
B. the extension in copper and steel parts will be in the ratio `1:2`
C. the stress applied to copper rod will be more
D. no extension will be produced in the steel rod

Answer

A, B, C

Explanation

`("stress")_(S)=F/(2A)("stress")_(Cu)=F/A`
Given that `(Y_(S))/(Y_(Cu))=2/1`
`("strain")/(("strain"_(Cu)))=((("stress")_(S))//(Y_(S)))/(("stress")_(Cu)//Y_(Cu))`
`(("stress")_(S))/(("stress")_(Cu))xxY_(Cu)/(Y_(S))=((F//2A))/((F//A))xx1/2=1/4`
`(L_(S)///_\L_(S))/(L_(Cu)///_\L_(Cu))=1/4` or `(L_(S)///_\L_(Cu))/(L_(Cu)///_\L_(S))=1/4`
`25/50xx(/_\L_(Cu))/(/_\L_(S))_=1/4` or `(/_\L_(Cu))/(/_\L_(S))=1/2`
So, options a, b and c are correct.