A particle of mass 100 g moving at an initial speed u collides with another particle of same mass kept initially at rest. If the total kinetic energy becomes 0.2 J after the collision, what could be the minimum and the maximum value of u.

Given: particle of mass m= 100g


Initial speed is u


Kinetic energy after collision is 0.2J


Then, Initial kinetic energy will be



Now,



Where is the final speed of first block,


is the final speed of second block.


v1+v2=u ----------- (1)


(v1 – v2) + L (a1-u2) =0


As u1= u and u2= 0


La1= (v2-v1) ------------ (2)


Adding equation (1) and (2)






Total kinetic energy after collision =0.2J




Putting values of v1 and v2




For maximum value of u denominator should be minimum


L=0


u2= 8


u = 2√2 m/s


For minimum value of u denominator should be maximum


L=1


u2=4


u = 2m/s


So, the minimum and the maximum value of u is 2 m/s and 2√2 m/s respectively.


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