In the ratio of diameters, lengths and Young's modulus of steel and copper wires shown in the figure are p, q and s respectively, then the corresponding ratio of increase in their length would be:

Step-by-step solution

We know that Young's modulus aligned & = FL 4 ~L & = 4 FL D ^2 4 ~L L & = 4 FL D ^2 ~L aligned According to questions. aligned & L _ S L _ C = F _ S F _ C L _ S L _ C D _ C ^2 ~L _ S D _ S ^2 ~L _ C & Here F _ S =(5 ~m +2 ~m ) g =7 mg & F _ C =5 mg ,=?, D _ S D _ C =P, & L _ S L _ C = S aligned Putting in eq. (ii) aligned L _ S L _ C & = 7 mg 5 mg q+ ( 1 P )^2 ( 1 ~S ) & = 7 q 5 p^2 ~S aligned