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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)mK
We know that, the time period of oscillation T=2πmk
The time period for which the block is in contact with the spring t=πmk ........(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=2ll2km=4mk
The Total time period of motion t=t1+t2
=πmk+4mk
=mk[π+4]
Hence, option (b) is the correct answer.

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