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:
(A) 10³ Nm⁻²
(B) 10⁶ Nm⁻²
(C) 10⁸ Nm⁻²
(D) 10⁴ Nm⁻²

Answer 1

Answer:

B options is Right Answer

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Answer 2

Thus the young's modulus of the rubber is Y =  3 x 10^6 Nm^-2

Option (B) is correct.

Explanation:

Given data:

• Length of the rubber = 42 cm
• Diameter of cross section area = 6 mm
• Weight of stone = 0.02 Kg
• Stretch in cord = 20 cm
• Velocity of stone = 20 ms^-1

Solution:

Energy of catapult = 1 / 2×(Δℓ / ℓ)^2 × Y × A × ℓ

Energy of catapult = Kinetic energy of the ball = 1 / 2 m v^2

therefore:

1 / 2 × (20 / 42)^2 × Y × π × 3^2 × 10^−6 × 42 × 10^−2 = 1/2 x 2 x 10^-2 x (20)^2

Y =  3 x 10^6 Nm^-2

Thus the young's modulus of the rubber is Y =  3 x 10^6 Nm^-2