A body of mass 2kg is placed on a horizontal frictionless surface. It is connected to one end of a spring whose force constant is 
. The other end of the spring is joined with the wall. A particle of mass 0.15kg moving horizontally with speed v sticks to the body after collision. If it compresses the spring by 
, the velocity of the particle is
Text Solution
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By the conservation of momentum
Initial momentum of particle = Final momentum of system ⇒ ⇒ m × × v = (m + M) V
∴ ∴ velocity of system 
Now the spring compresses due to kinetic energy of the system so by the conservation of energy
⇒ ⇒ 
Putting m = 0.15 kg, M = 2 kg, k = 250 N/m, x = 0.1 m we get v = 15 m/s.
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