Q. 214.2( 20 Votes )

# Two objects of masses 100 g and 200 g are moving along the same line and direction with velocities of 2 ms^{-1} and 1 ms^{-1}, respectively. They collide and after the collision, the first object moves at a velocity of 1.67 m s^{-1}. Determine the velocity of the second object.

Answer :

For this, firstly we have to calculate the total momentum of both the objects:

Momentum of first object:

= Mass of first object × Velocity of first object

= kg × 2 m/s

= 0.1 kg × 2 m/s

= 0.2 kg m/s

Momentum of second object:

= Mass of second object × velocity of object

= kg × 1 m/s

= 0.2 kg × 1 m/s

= 0.2 kg m/s

Total momentum = Momentum of first object + Momentum of second object

= 0.2 + 0.2

= 0.4 kg m/s

It is given that after the collision, the velocity of first object becomes 1.67 m/s

Momentum after collision (First object):

= kg × 1.67 m/s

= 0.1 kg × 1.67 m/s

= 0.167 kg m/s

Let, the velocity of second object after the collision be v m/s

Momentum after collision (Second object)

= kg × *v* m/s

= 0.2 kg × *v* m/s

= 0.2*v* kg m/s(ii)

Total momentum of the objects after collision = 0.167 + 0.2 *v*

We know that,

According to the law of conversion of momentum:

Total momentum before collision = Total momentum after collision

0.4 = 0.167 + 0.2 *v*

0.2 *v* = 0.4 – 0.167

0.2 *v* = 0.233

v =

v = 1.165 m/s

Therefore, the velocity of second object will be 1.165 m/s

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