A metal rod consumes power P on passing current. If it is cut into...

Let the resistance of the rod be $R$. If the rod is divided into two equal parts, then each part of the rod will have a resistance of $R / 2$. Now these two parts of the rod are connected in parallel and a voltage $V$ is applied across them. Hence the total power consumed is $$P^{\prime}=$\frac{V^2}{R / 2}+\frac{V^2}{R / 2}=$4$\frac{V^2}{R}=$4 P$\text{where } P=\frac{V^2}{R}$is the power consumed by the original rod when voltage$V$ is applied across it.