# Two objects of masses 100g and 200g are moving along the same line in the same direction with velocities of 2m//s and 1m//s, respectively. The

57 views
in Physics
closed
Two objects of masses 100g and 200g are moving along the same line in the same direction with velocities of 2m//s and 1m//s, respectively. They collide and after the collison, the first object moves at a velocity of 1.67 m//s in the same direction. Determine the velocity of the second object.

by (66.1k points)
selected by

In order to solve this problem, we will first calculate total momentum of both the objects before and after the collision.
Momentum of first object (before collision)=Mass of first objectxxVelocity of first object
=100/1000kgxx2ms^(-1)
0.1kgxx2ms^(-1)
=0.2 kg ms^(-1)
Momentum of second object (before collision) = Mass of second objectxx Velocity of second object
=200/1000kgxx1ms^(-1)
=0.2kgms^(-1)
Total momentum = 0.2 + 0.2
(before collision)=-04 kg m s^(-1)
(b) After collision, the velocity of first object of mass 100 g becomes 1.67 m s^(-1). So,
Momentum of first object (after collision)=100/1000kgxx1.67ms^(-1)
=0.1kgxx1.67ms^(-1)
=0.167kgms^(-1)
After collision, suppose the velocity of second object of mass 200 g becomes vms^(-1). So,
Momentum of second object (after collision)=200/1000kgxxvms^(-1)
=0.2kgxxvms^(-1)
=0.2vkgms^(-1)
Total momentum (after collision)=0.167+0.2 v
Now, according to the law of conservation of momentum :
Total momentum before collision=Total collision after collision
That is, 0.4=0.167+0.2v
0.2v=0.4-0.167
0.2v=0.233
v=0.233/0.2
v=1.165ms^(-1)
Thus, the velocity of second object is 1.165 metres per second.