A particle of mass m moving in the x-direction with speed 2 v is hit by another particle of mass 2 m moving in the y-direction with speed v . If the collision is perfectly inelastic, what is the percentage loss in the energy during the collision (to the closest integer value)?

Step-by-step solution

The initial momentum of system is P i → = m 2 V i ^ + 2 m V j ^ According to question as On perfectly inelastic collision the particles stick to each other. P f → = 3 m V f → By conservation of linear momentum P f → = P i → ⇒ 3 m V f → = m 2 V i ^ + 2 m V j ^ ⇒ V f → = 2 V 3 i ^ + j ^ ⇒ | V f | = 2 2 3 V ∴ loss in KE. of system = K i n i t i a l - K f i n a l = 1 2 m 2 V 2 + 1 2 2 m V 2 - 1 2 3 m 2 2 V ⁡ 3 2 = 2 m V 2 + m V 2 - 4 3 m V 2 = 3 m V 2 - 4 m V 2 3 = 5 3 m V 2 % Loss in KE = 100 × ∆ K K i = 5 3 m v 2 3 m