Question

# A particle of mass 100g moving at an initial spped u collides with another particle of same mass kept initially at rest. If the total kinetic energy becomes 0.5J after the collision, what could be the minimum and the maximum value of u.

A
2 m/s, 4 m/s
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B
2 m/s, 22m/s
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C
22m/s , 2 m/s
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D
2 m/s ,2 m/s
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Solution

## The correct option is B 2 m/s, 2√2m/sFinal K.E. = 0.2J Initial K.E. =12mV21+0=12×0.1 u2=0.05 u2 mv1=mv′2=mu Where v1 and v2 are final velocities of 1st and 2nd block respectively. ⇒v1+v2=u . . . (1) (v1−v2)+t(a1−u2)=0⇒ta=v2−v1 . . . (2) u2=0, u1=u Adding Eq.(1) and Eq.(2) 2v2=(1+l)u⇒v2=(u2)(1+l) ∴ v1=u−u2−u2l v1=u2(1−l) Given (12)mv21+(12)mv22=0.2 ⇒v21+v22=4 ⇒u24(1−l)2+U24(1+l)2=4 ⇒u22(1+l2)=4 ⇒u2=81+l2 For maximum value of u, denominator should be minimum, ⇒ l=0 ⇒u2=8⇒u=2√2m/s For minimum value of u, denominator should be maximum, ⇒l=1 u2=4⇒u=2m/s

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