The rubber cord of catapult has a cross-sectional area 1 ${\mathrm{mm}}^2$ and total unstretched length 10.0 cm. It is stretched to 12.0 cm and then released to project a missile of mass 5.0 g. Taking young's modulus Y for rubber as $5.0 \times {10}^8 {\mathrm{Nm}}^2$. Total elastic energy of catapult is converted into kinetic energy of missile without any heart loss. The velocity of projection is

detailed solution

Correct option is A

Total elastic energy of catapult is converted into kinetic energy of missile without any heat loss.Elastic energy = 12×load×extensionHere extension,∆L = 12.0 - 10.0 = 2.0 cm = 2.0 ×10-2 mFrom relation Y = FLA∆LLoad, F = YA∆LL             = = 5.0×108×1×10-6×2.0×10-210.0 × 10-2 = 100 NIf v is velocity of projection, we haveElastic energy of catapult = kinetic energy of missilei.e., 12×load×extension = 12mv2     12×100×2.0×10-2 = 12×(5.0×10-3)v2This gives v2 = 100×10-2×25×10-3 = 400v = 400  = 20 m/s