When rubber cord is stretched, then it stores potential energy and when released, this potential energy is given to the stone as kinetic energy.

So, potential energy of stretched cord = kinetic energy of stone

$$ \Rightarrow {1 \over 2}Y{\left( {{{\Delta L} \over L}} \right)^2}A\,.\,L = {1 \over 2}m{v^2}$$

Here, $$\Delta$$L = 20 cm = 0.2 m, L = 42 cm = 0.42 m, v = 20 ms^$$-$$1, m = 0.02 kg, d = 6 mm = 6 $$\times$$ 10^$$-$$3 m

$$\therefore$$ $$A = \pi {r^2} = \pi {\left( {{d \over 2}} \right)^2} = \pi {\left( {{{6 \times {{10}^{ - 3}}} \over 2}} \right)^2}$$

$$ = \pi {(3 \times {10^{ - 3}})^2} = 9\pi \times {10^{ - 6}}{m^2}$$

On substituting values, we get

$$Y = {{m{v^2}L} \over {A{{(\Delta L)}^2}}} = {{0.02 \times {{(20)}^2} \times 0.42} \over {9\pi \times {{10}^{ - 6}} \times {{(0.2)}^2}}}$$

$$ \approx 3.0 \times {10^6}N{m^{ - 2}}$$

So, the closest value of Young's modulus is 10⁶ Nm^$$-$$2.