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 object`xx`Velocity of first object

`=100/1000kgxx2ms^(-1)`

`0.1kgxx2ms^(-1)`

`=0.2 kg ms^(-1)`

Momentum of second object (before collision) = Mass of second object`xx` 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 v`ms^(-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.