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Home / Doubts and Solutions/ICSE/Class 11 Science/Physics

A,an object mass is 100g the another object B mass is 400g this two object velocity are 100cm/s and 10 cm/s they are moving along the same line and collided each other. After collusion which direction they go and how much distance will exceed they are in 10 second 

Asked by parthasarathiacharjee672 12th May 2019, 10:29 AM
Answered by Expert
Answer:
Let m1 = 100 g   and  v1i = 100 cm/s  are the mass and initial velocity of object 1.
 
Let m2 = 400 g   and  v2i = 10 cm/s  are the mass and initial velocity of object 2.
 
Let v1f   and v2f are final velocities of object-1 and object-2 respectively.
 
It is assumed collision is elastic
 
By Conservation of momntum :-  m1 v1i  + m2 v2i  = m1 v1f  + m2 v2f
 
100×100 + 400×10 = 100 v1f  + 400 v2f   or   v1f  + 4 v2f = 140  ....................(1)
 
By consevation of energy :-  (1/2) m1 v1i2  + (1/2) m2 v2i2  = (1/2) m1 v1f2  + (1/2) m2 v2f2
 
100×100×100 + 400×10×10 = 100× v1f2  + 400× v2f2   or  v1f2  + 4 v2f2 = 10400  .....................(2)

using eqn.(1), we can substitute for v1f  in eqn.(2) to get,   (140 - v2f )2 + 4 v2f2 = 10400  ...............(3)
 
eqn.(3) can be simplified as,   v2f2 - 56 v2f + 460  = 0     .....................(4)
 
physically valid solution of eqn.(4) is  v2f = 46 cm/s .     from eqn.(1) we get v1f = -44 cm/s
(Other solution v2f = 10 cm/s is not valid, because after collision there is no change of velocities )
 
Hence object-1 will move in same direction with velocity 46 cm/s  ,
 
but object-2 will move in opposite direction with velocity -44 cm/s.
 
10 seconds after collision, distance between them = 46×10 + 44×10 = 900 cm
Answered by Expert 12th May 2019, 4:26 PM
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