Two particles of equal mass m have respective initial velocities u i ^ and u i ^ + j ^ 2 . They collide…

Two particles of equal mass m have respective initial velocities ui^ and ui^+j^2 . They collide completely inelastically. The energy lost in the process is:
  1. 13mu2
  2. 18mu2
  3. 34mu2
  4. 23mu2

Solution

Conserving momentum
mui^+mu2i^+u2j^=2mu1i^+u2j^
On solving
u1=3u4 and u2=u4
Change in K.E.
12mu2+12mu222-122m9u216+u216
=3mu24-5mu28=mu28

Asked in: JEE Main 2020 (09 Jan Shift 1)

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