A boy’s catapult is made of rubber cord which is 42 c m long, with 6 m m diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02 k g on it and stretches the cord by 20 c m 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:

Question

A boy’s catapult is made of rubber cord which is 42 c m long, with 6 m m diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02 k g on it and stretches the cord by 20 c m 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:, 10 6 N m - 2, 10 4 N m - 2, 10 8 N m - 2, 10 3 N m - 2

MARKS App · Accepted Answer

Elastic potential energy = 1 2 . Y . ∆ l L 2 A L = 1 2 Y . 0.2 0.42 2 . π × 3 2 × 10 - 6 × 0.42 = 1.35 × 10 - 6 Y Kinetic energy = 1 2 m v 2 = 1 2 × ( 0.02 × 20 2 ) 1.35 × 10 - 6 Y = 4 Y = 3 × 10 6 N m - 2

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