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A boy's catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02 kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of 20 m s⁻¹. Neglect the change in the area of cross-section of the cord while stretched. The Young's modulus of rubber is closest to -

1. 10³ N m⁻²
2. 10⁴ N m⁻²
3. 10⁶ N m⁻²
4. 10⁸ N m⁻²

Correct answer: 10⁶ N m⁻²

Solution

A = pi*(0.003)^2 = 2.83e-5 m^2. Y = m v^2 L /(A * dL^2) = (0.02*400*0.42)/(2.83e-5 * 0.04) ~ 3e6 N/m^2, i.e. order 10^6.

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