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Question

A block of mass m compresses a spring of stiffness constant k and natural length l, through a distance l2 as shown in the figure. If the block is not fixed with the spring, the period of motion of the block is [Assume collision to be elastic with the wall and horizontal surface to be smooth]

A
2πmK
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B
(π+4)mK
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C
(1+π)mk
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D
None of these
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Solution

The correct option is B (π+4)√mKWe know that, the time period of oscillation T=2π√mk The time period for which the block is in contact with the spring t=π√mk ........(1) After which,it leaves the spring with a speed v=ω A From the data given in the question, v=(√km)(l2) .......(2) Since the floor is frictionless, it moves with constant velocity v for a distance D=l+l=2l Corresponding time taken during the motion t2=2l/v Using (2) in the above equation we get, t2=2ll2√km=4√mk ∴ The Total time period of motion t=t1+t2 =π√mk+4√mk =√mk[π+4] Hence, option (b) is the correct answer.

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