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Q.

A system consists of two identical cubes, each of mass 3 kg, linked together by a compressed weightless spring of force constant 1000 N m-1. The cubes are also connected by a thread which is burnt at a certain moment. At what minimum value of initial compression x0 (in cm) of the spring will the lower cube bounce up after the thread is burnt through?

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answer is 9.

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Detailed Solution

Let x be the elongation in the spring when it returns back. 12kx02=12kx2+mgx+x0kx2+2mgx+2mgx0-kx02=0On solving, we get x=-2mg±2mg2-4k2mgx0-kx022kkx=−mg±kx0-mg=−2mg+kx0(ignoring negative sign)        …………..(i)And also lower block will bounce up if        kx≥mg⇒−2mg+kx0≥mgSo  x0=3mgk⇒x0=9 cm
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