Question

The rubber cord catapult has a cross-section area 1 mm² and total unstretched length 10 cm. It is stretched to 12 cm and then released to project a stone of mass 5 gm. Taking Young’s modulus Y of rubber as 5 × 10⁸ N/m², the velocity of projection will be –

• A. 20 cm/s
• B. 20 m/s
• C. 2 m/s
• D. None of these

Answer 1

Answer: (B)

20 m/s

Answer 2

P.E. = $\frac{Y}{2}$ (strain)² (AL) = K.E. = $\frac{1}{2}$ mv²

v = strain $\sqrt{\frac{Y}{m}AL}$

= $\frac{2}{10}$ $\sqrt{\frac{5 \times 10^{8}}{5 \times 10^{–3}} \times 10^{–6} \times 0.1}$

= 20 m/s