Momentum and CollisionHard
Question
Two blocks A and B each of mass m, are connected by a massless spring of natural length L and spring constant k. The block initially resting on a smooth horizontal floor with the spring at its natural length, as shown in figure. A third identical block C, also of mass m move on the floor with a speed v along the joining A and B, and collides elastically with A. Then
Options
A.the kinetic energy of the A-B system, at maximum compression of the spring, is zero
B.the kinetic energy of the A-B system, at maximum compression of the spring, is mv2/4
C.the maximum compression of the spring is v
D.the maximum compression of the spring is v
Solution
After collision between C and A, C stop while A moves with speed of C i.e., v [in head on elastic collision, two eaual masses exchange their velocities] At maximum compression , A and B will move with same speed v/2 (From conservation of linear momentum).
Let x be the maximum compression in this position
or Kmax = mv2 / 4From conservation of mechanical energy in two positions shown in figure.
v2
∴ Correct option is (b).
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