Q.

A block (B) is attached to two unstretched springs S1 and S2 with spring constants k and 4k respectively (fig i). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have negligible mass. There is no friction any where.  The block B is displaced towards wall 1 by a small distance x (fig, ii) and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are measured with respect to the equilibrium position of the block B. The ratio y/x is 

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a

2

b

1/4

c

1/2

d

4

answer is C.

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Detailed Solution

One end of each spring is fixed to block B while other end is fixed to freely movable plates M1 and M2. When the block is displaced by x towards left, compression in S1 is x while S2 is in its relaxed position and when block moves a distance y in opposite direction measured from equilibrium position, compression in spring S2 is y and spring S1 is in its natural position. As y is maximum distance towards wall 2, the kinetic energy of block at this location is zero. Applying energy conservation at two locations, kx22=4ky22 or yx=12

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