A particle of mass m is moving along the x-axis with initial velocity  ui^. It collides elastically with a particle of mass 10m at rest and then moves with half its initial kinetic energy, (see figure). If sinθ1=nsinθ2  then value of n is

Given→12MV12=1212Mu2    ⇒V1=u2From conservation of momentum in y – direction V1sinθ1=10V2sinθ2→1  As collision is elastic KE remains conserved 12Mu2=12MV12+1210MV22⇒12Mu2=1212Mu2+1210MV22 ⇒14Mu2=102MV22 ⇒u220=V22 ⇒V2=u20 Put in equation (1)⇒u2sinθ1=10u20sinθ2  ⇒sinθ1=10sinθ2