First slide
Collisions
Question

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/s
b) Momentum of 5kg mass after collision is  4kg m/s
c) Kinetic energy of the centre of mass 12total massvcm2 is  0.75 J
d) Total kinetic energy of the system is 4J 
 

Moderate
Solution

Given point
Mass of  m=1kg
Mass of stationary point m=5kg  
Speed  v=2m/s
By conservation of linear momentum

u=5v2...i

2. As we know, the coefficient of restitution is given by e=v2v1u1u2=1  for elastic collision. Using this we get,  u=v+2....ii
Using Equation (i) and (ii), we have  v=1 m/s and  u=3 m/s

Initial momentum of the system,  m1u1=(1)3=3kgm/s

v2=2m1u1m1+m2=2(1)31+5=1 KE of 5kg =12m2v22=12(5)(1)2=2.5J

Vcom=m1u1+m2u2m1+m2=1(3)+5(0)1+5=36=12m/s
Kinetic energy of the centre of mass  =12msystemvCM2=121+5122=0.75 J

KE of system=12m1v12+12m2v22=12(1)(3)2+12(5)(0)2=4.5J
Therefore, the correct answer is (B).
 


 

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