A sphere P of mass m and velocity v_i undergoes an oblique and perfectly elastic collision with an identical sphere Q initially at rest. The angle theta between the velocities of the spheres after the collision shall be

A sphere P of mass m and velocity v_i undergoes an oblique and perfect

1.	A sphere P of mass m and velocity v_i undergoes an oblique and perfectly elastic collision with an identical sphere Q initially at rest. The angle theta between the velocities of the spheres after the collision shall be
Answer» 0 `45^@` `90^@` `180^@` SOLUTION :According to law of conservation of linear momentum , we get `mvecv_i+mxx0=mvecv_(Pf)=mvecv_(Qf)` where `vecv_(Pf) and vecv_(Qf)` are the final VELOCITIES of SPHERES P and Q after collision respectively. `vecv_i=vecv_(Pf)+vev_(Qf)` `(vecv_i.vecv_i)=(vecv_(Pf)+vecv_(Qf)).(vecv_(Pf)+vecv_(Qf))` `vecv_(Pf). vecv_(Pf)+vecv_(Qf). vecv_(Qf)+2vecv_(Pf). vecv_(Qf)` or `v_i^2=v_(Pf)^2+v_(Qf)^2 + 2v_(Pf) v_(Qf) cos theta`...(i) According to conservation of kinetic energy , we get `1/2mv_i^2 =1/2mv_(Pf)^2 + 1/2mv_(Qf)^2 implies v_i^2=v_(Pf)^2 +v_(Qf)^2`...(ii) Comparing (i) and (ii), we get `2v_(Pf)v_(qf)cos theta=0 implies cos theta =0 or theta=90^@`