Two wires are made of the same material and have the same volume. The first wire has cross-sectional area $$A$$ and the second wire has cross-sectional area $$3 A$$. If the length of the first wire is increased by $$\Delta l$$ on applying a force $$F$$, how much force is needed to stretch the second wire by the same amount?

A man grows into a giant such that his height increases to 8 times his original height. Assuming that his density remains same, the stress in the leg will change by a factor of

A spring of force constant $$k$$ is cut into lengths of ratio $$1:3:4$$. They are connected in series and the new force constant is $$\mathrm{k}$$'. Then they are connected in parallel and force constant is $$\mathrm{k}$$''. Then $$\mathrm{k}^{\prime}: \mathrm{k}^{\prime \prime}$$ is

A copper and a steel wire of same diameter are connected end to end. A deforming force F$$_1$$ is applied to the wire which causes an elongation of 1 cm. The two wires will have