• # question_answer Two particles, of masses M and 2M, moving, as shown, with speeds of 10 m/s and 5 m/s, collide elastically at the origin. After the collision, they move along the indicated directions with speeds${{\upsilon }_{1}}$and ${{\upsilon }_{2}}$, respectively. The values of ${{\upsilon }_{1}}$and ${{\upsilon }_{2}}$ are nearly: [JEE Main 10-4-2019 Morning] A) 3.2 m/s and 6.3 m/sB) 3.2 m/s and 12.6 m/sC) 6.5 m/s and 6.3 m/sD) 6.5 m/s and 3.2 m/s

$M\times 10\cos {{30}^{o}}+2M\times 5\cos {{45}^{o}}$           $=2M\times {{\text{v}}_{1}}\cos {{30}^{o}}+M\,{{\text{v}}_{2}}\cos {{45}^{o}}$    $5\sqrt{3}+5\sqrt{2}=2{{\text{v}}_{1}}\frac{\sqrt{3}}{2}+\frac{{{\text{v}}_{2}}}{\sqrt{2}}$           $10\times \text{ }M\text{ sin }30{}^\circ 2M\times 5\text{ sin }45{}^\circ$ $=M\text{ }{{\text{v}}_{2}}\text{ sin }45{}^\circ 2M\text{ }{{\text{v}}_{1}}\text{ sin }30{}^\circ$ $5-5\sqrt{2}=\frac{{{\text{v}}_{2}}}{\sqrt{2}}-{{\text{v}}_{1}}$ Solving ${{\text{v}}_{1}}=\frac{17.5}{2.7}\simeq 6.5m/s$ ${{\text{v}}_{2}}\approx 6.3\,m/s$