A \(20 \mathrm{~kg}\) block resting on the floor is to be raised by a \(5.0-\mathrm{mm}-\) diameter rope with Young's modulus \(1.5 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}\). The rope goes up and over a pulley that is \(2.5 \mathrm{~m}\) above the floor. You hold the rope at a point \(1.5 \mathrm{~m}\) above the floor and pull hard enough to lift the block just off the floor. By how much does the rope stretch?

A. \(3.0 \mathrm{~mm}\)

B. \(6.3 \mathrm{~mm}\)

C. \(9.3 \mathrm{~mm}\)

D. \(13 \mathrm{~mm}\)