The rubber cord catapult has a cross-sectional area of 1 mm2 and a total unstretched length of 10 cm. It is stretched to 12 cm and then released to project a stone of mass 5 g. Taking Young's modulus Y of rubber as 5 x 10^8 N/m2, the velocity of projection will be:
Correct answer: B. 20 m/s
- A. 20 cm/s
- B. 20 m/s
- C. 2 m/s
- D. None of these
Explanation
The potential energy stored in the stretched rubber cord is given by the formula U = (1/2) × Y × (A/L) × ΔL2, where Y is Young's modulus, A is the cross-sectional area, L is the original length, and ΔL is the change in length. Substituting the given values: U = (1/2) × 5 × 108 N/m2 × (1 × 10-6 m2 / 0.1 m) × (0.02 m)2. Calculating this gives us the potential energy. The kinetic energy of the stone when projected is (1/2)mv2, where m is the mass of the stone and v is its velocity. Equating the potential energy to kinetic energy and solving for v gives us v = 20 m/s. Other options are incorrect due to either incorrect calculations or unit conversion errors.
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