A ball of mass $$0.2 \mathrm{~kg}$$ is thrown vertically down from a height of $$10 \mathrm{~m}$$. It collides with the floor and loses $$50 \%$$ of its energy and then rises back to the same height. The value of its initial velocity is

A smooth chain of length $$2 \mathrm{~m}$$ is kept on a table such that its length of $$60 \mathrm{~cm}$$ hangs freely from the edge of the table. The total mass of the chain is $$4 \mathrm{~kg}$$. The work done in pulling the entire chain on the table is (Take, $$g=10 \mathrm{~m} / \mathrm{s}^2$$)

A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time $$t$$ is proportional to