A light string attached to a bead passing over a smooth fixed pulley at a distance of  $d=15\text{ m}$ from the vertical rod as shown in the figure. At the other end of the string a block of mass $1\text{ kg}$ is attached, lying over a smooth fixed inclined plane of inclination angle  ${37}^{\circ }$. Mass of the bead is $1\text{ kg}$ and friction between bead and vertical rod is zero. The bead is held in level with the pulley and released. If the speed of the bead when the string between bead and pulley makes an angle  ${53}^{\circ }$ with the horizontal is  $\sqrt{\frac{\alpha \times 1000}{41}}\text{ m}/\text{s}$, find value of  $\alpha$. [take  $g=10{\text{ m/s}}^2$]