A block `(B)` is attached to two unstriched sprig `S_(1)` and S_(2) with spring constant `K` and `4K` , respectively (see fig 1) The other ends are atteched in identical support `M_(1)` and `M_(2)` not attached in the walls . The springs and supports have negligible mass . There is no friction anywhere . The block `B` is displaced toword wall `1` by a small distance `z` (figure (ii)) and released . THe block return and moves a maximum displacements `x` and `y` are musured with reoact to the equalibrum of the block `B` and the ratio `y//x` is

Options

A. `4`
B. `2`
C. `1//2`
D. `1//4`

Answer

C

Explanation

One end of each spring is fixed to block `B` while other end is fixed to freely movable plates `M_(1)` and `M_(2)`. When the block is displaced by `x` towards left, compression in `S_(1)` is `x` while `S_(2)` is in its relaxed position and when block moves a distance `y` in opposite direction measured form equilibrium position, compression is spring `S_(2)` is `y` and spring `S_(1)` is in its natural position. As `y` is maximum distance towards wall `2`, the kinwtic enegry of block at this location is zero. Applying enegry conservation at two locations, `(kx^(2))/(2) =(4ky^(2))/(2) or (y)/(x) = (1)/(2)`