Centre of Mass 2 Question 8
9. Two bodies and of masses and respectively are placed on a smooth floor. They are connected by a spring. A third body of mass moves with velocity along the line joining and and collides elastically with as shown in figure. At a certain instant of time after collision, it is found that the instantaneous velocities of and are the same. Further at this instant the compression of the spring is found to be . Determine (a) the common velocity of and at time and (b) the spring constant.
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Answer:
Correct Answer: 9. (a)
(b)
Solution:
- (a) Collision between
and is elastic and mass of both the blocks is same. Therefore, they will exchange their velocities i.e. will come to rest and will be moving will velocity . Let be the common velocity of and , then from conservation of linear momentum, we have
(a)
At rest
(b)
(c)
(b) From conservation of energy, we have