The correct answer is $\boxed{\text{B) 1000 cum}}$.
Let $x$ be the quantity of earth for which the cost of excavation by machine will be equal to the cost of manual excavation. We know that the cost of manual excavation is Rs. 10 per cum, so the cost of excavating $x$ cum by hand is $10x$. The cost of excavating $x$ cum by machine is a fixed cost of Rs. 4000 plus a variable cost of Rs. 2 per cum, so the cost of excavating $x$ cum by machine is $4000 + 2x$. We are told that the cost of excavation by machine is equal to the cost of manual excavation, so we have the equation $10x = 4000 + 2x$. Solving for $x$, we get $x = 1000$.
Option A is incorrect because 500 cum is not enough earth to make the cost of excavation by machine equal to the cost of manual excavation. Option C is incorrect because 1500 cum is not enough earth to make the cost of excavation by machine equal to the cost of manual excavation. Option D is incorrect because 2000 cum is not enough earth to make the cost of excavation by machine equal to the cost of manual excavation.