A point mass of 1kg collides elastically with a stationary point mass of  5kg. After their collision, the 1kg  mass reverses its direction and moves with a speed of  2m/s. Which of the following statement(s) is (are) correct for the system of these two masses?a) Total momentum of the system is  3kg m/sb) Momentum of 5kg mass after collision is  4kg m/sc) Kinetic energy of the centre of mass 12 total massvcm2 is  0.75 Jd) Total kinetic energy of the system is 4J

Given pointMass of  m=1kgMass of stationary point m=5kg  Speed  v=2m/sBy conservation of linear momentumu=5v−2...i2. As we know, the coefficient of restitution is given by e=v2−v1u1−u2=1  for elastic collision. Using this we get,  u=v+2....iiUsing Equation (i) and (ii), we have  v=1 m/s and  u=3 m/sInitial momentum of the system,  m1u1=(1)3=3kgm/sv2=2m1u1m1+m2=2(1)31+5=1 ⇒KE of 5kg =12m2v22=12(5)(1)2=2.5JVcom=m1u1+m2u2m1+m2=1(3)+5(0)1+5=36=12m/sKinetic energy of the centre of mass  =12msystemvCM2=121+5122=0.75 JKE of system=12m1v12+12m2v22=12(1)(3)2+12(5)(0)2=4.5JTherefore, the correct answer is (B).