A wind-powered generator converts wind energy into electric energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electric energy. For wind speed $v$, 89 the electric power output will be proportional to

A spring, which is initially in its unstretched condition, is first stretched by a length $x$ and then again by a further length $x$. The work done in the first case is $W_1$, and in the second case is $W_2$. Then

A ball is released from the top of a tower. The ratio of work done by force of gravity in first, second and third second of the motion of the ball is

When a force is applied on a moving body, its motion is retarded. Then the work done is

A uniform chain of length $2 \mathrm{m}$ is kept on a table such that a length of $60 \mathrm{cm}$ hangs freely from the edge of the table. The total mass of the chain is $4 \mathrm{kg}$. What is the work done in pulling the entire chain in the table?

A particle of mass $m$ moving in a horizontal plane ($x-y$) along the x-axis, at a certain height above the ground. It suddenly explodes into two fragments of masses $\frac{m}{4}$ and $\frac{3m}{4}$. An instant later, the smaller fragment is at $y=+15 \mathrm{cm}$. The larger fragment at this instant is at

Two identical cylindrical vessels, with their bases at the same level, each contains a liquid of density $\rho$. The height of the liquid in one vessel is $h_1$ and that on the other is $h_2$. The area of either base is $A$. What is the work done by gravity in equalizing the levels when the vessels are interconnected?