Prove that : $\sf (i) \; \dfrac{ {a}^{-1}}{{a}^{-1} + {b}^{-1}} + \dfrac{{a}^{-1}}{{a}^{-1} - {b}^{-1}} = \dfrac{2b^2}{b^2 - a^2}$ $\sf (ii) \; \dfrac{a+b+c}{{a}^{-1}{b}^{-1}+{b}^{-1}{c}^{-1} + {c}^{-1}{a}^{-1}}=abc$ ...

A bucket of water tied to a rope is being pulled up from a well as shown in the figure below (fig 1). Name the two forces acting on the bucket in the upward and downward directions. Also mention whether these forces are contact or non-contact forces by nature.​

A bucket of water tied to a rope is being pulled up from a well as shown in the figure below (fig 1). Name the two forces acting on the bucket in the upward and downward directions. Also mention whether these forces are contact or non-contact forces by nature.