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

( c) When the block `B` is displaced toward well `1` , only spring `S_(1) ` is compressed and `S_(2) ` is its natural same . This happens because this ofter end of `S_(2)` is not atteched to the will hat is free . Therefor the energy stored in the systen `= (1)/(2)k_(1)x^(2)` when the block is will come back to the equlitbrum position and move toward well 2 As the happeens the spring `S_(1)` comes in its nature length and `S_(2)` gas compressed . As there are so frictional force invalved , the P E sound is the `S_(1)` gas street and at the PE of spring `s_(1) ` when the block `B` its extreme posion after compressed `s_(2)` by `y`
` :. (1)/(2) k_(1) x^(2) = (1)/(2) k_(2) y^(2)`
`(1)/(2) xx kx^(2) = (1)/(2) 4 ky^(2) , x^(2) = 4y^(2) :. (y)/(x) = (1)/(2)`