JEE MAINS PHYSICS QUESTION SEPTEMBER 2020
Answers
A body of mass m moving with velocity v collides with shown masses respectively. find loss in kinetic energy after the last collision. consider all collision completely inelastically. ?
solution : as collisions are being considered completely inelastically.
so after final collision, all bodies move together. let final velocity of system of bodies is v'
from conservation of linear momentum.
initial momentum = final momentum
⇒mv = (m + m + 2m + 4m + 8m)v'
⇒v/16 = v'
now loss in kinetic energy , ∆K = initial kinetic energy - final kinetic energy
= 1/2 mv² - 1/2 (16m)(v/16)²
= 1/2 mv²[1 - 1/16]
= 1/2 mv² (15/16)
now percentage loss in kinetic energy after the last collision = ∆K/K_i × 100
= 1/2 mv²(15/16)/1/2 mv² × 100
= (15/16) × 100
= 15 × 25/4
= 375/4
= 93.75
Therefore the percentage loss in kinetic energy after the last collision is 93.75 %