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 0.02kg 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:
(1) 10^4 Nm-2
(2) 10^8 Nm-2
(3) 10^6 Nm-2
(4) 10^3 Nm-2​

Answer 1

Option  C is correct

10^6 Nm-2

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

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