Eduprobe
Question:
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
10^4 Nm^-2
10^3 Nm^-2
10^8 Nm^-2
10^6 Nm^-2
Solution:
Correct option is C. 10^6 Nm^-2
Energy of catapult = 1/2 × (Δl/l)^2 × Y × A × l = Kinetic energy of the ball = 1/2 mv^2
therefore, 1/2 × (20/42)^2 × Y × π × (3^2 × 10^-6) × 42 × 10^-2 = 1/2 × 2 × 10^-2 × (20)^2
Y ≈ 3 × 10^6 Nm^-2.