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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 ms-1. Neglect the change in the area of cross-section of the cord while stretched. The Young’s modulus of rubber is closest to:

(A) 106 N m-2

(B) 104 N m-2

(C) 108 N m-2

(D) 103 N m-2

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(A) 106 N m-2

d = 6 mm = 0.006 m, l = 42 cm = 0.42 m,

∆l = 20 cm = 0.2 m, m = 0.02 kg, v = 20 m/s

Energy stored in the catapult,

Energy stored in the catapult gives the kinetic energy to the stone.

= 3 × 106 N/m2

∴ Y is closest to 106 N m-2

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