Two wires A and B are of the same materials. Their lengths are in the ratio 1: 2 and diameters are in the ratio 2: 1 . When stretched by force F_ A and F_ R respectively they get equal increase in their lengths. Then the ratio F_ A / F_ B should be

Step-by-step solution

Force F= Y A l l Substituting area A= ( d 2 )²= d² 4 So, we have F= Y d² l 4 l F d² l l [ Y 4 = constant ] Hence, using Eq. (i), we have array l F_ A d_ A ² l_ A l_ A F_ B d_ B ² l_ B l_ B array From Eqs. (i) and (ii), we get F_ A F_ B = d_ A ² l_ A l_ A l_ B d_ B ² l_ B as l_ A = l_ B = l Therefore F_ A F_ B = d_ A ² d_ B ² l_ B l_ A Putting d_ A d_ B = 2 1 and l_ B l_ A = 2 1 we get F_ A : F_ B =8: 1