The rubber cord of catapult has a cross-sectional area 1 mm2 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 × 108 Nm2. Total elastic energy of catapult is converted into kinetic energy of missile without any heart loss. The velocity of projection is

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