Two wire of same material having radius in ratio 2 : 1 and lengths in ratio 1: 2. If same force is applied on them, then ratio of their change in length will be

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