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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. |
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Answer» 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. |
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