Centre of Mass 2 Question 8

9. Two bodies A and B of masses m and 2m respectively are placed on a smooth floor. They are connected by a spring. A third body C of mass m moves with velocity v0 along the line joining A and B and collides elastically with A as shown in figure. At a certain instant of time t0 after collision, it is found that the instantaneous velocities of A and B are the same. Further at this instant the compression of the spring is found to be x0. Determine (a) the common velocity of A and B at time t0 and (b) the spring constant.

(1984,6M)

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Answer:

Correct Answer: 9. (a) v03

(b) 2mv023x02

Solution:

  1. (a) Collision between A and C is elastic and mass of both the blocks is same. Therefore, they will exchange their velocities i.e. C will come to rest and A will be moving will velocity v0. Let v be the common velocity of A and B, then from conservation of linear momentum, we have

(a)

B

At rest

(b)

(c)

mAv0=(mA+mB)v or mv0=(m+2m)v or v=v03

(b) From conservation of energy, we have

12mAv02=12(mA+mB)v2+12kx02 or 12mv02=12(3m)v032+12kx02 or 12kx02=13mv02 or k=2mv023x02



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