| 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/s
B) 3.2 m/s and 12.6 m/s
C) 6.5 m/s and 6.3 m/s
D) 6.5 m/s and 3.2 m/s
Correct Answer: C
Solution :
| [c] \[M\times 10\cos {{30}^{o}}+2M\times 5\cos {{45}^{o}}\] |
| \[=2M\times {{\text{v}}_{1}}\cos {{30}^{o}}+M\,{{\text{v}}_{2}}\cos {{45}^{o}}\] |
| \[5\sqrt{3}+5\sqrt{2}=2{{\text{v}}_{1}}\frac{\sqrt{3}}{2}+\frac{{{\text{v}}_{2}}}{\sqrt{2}}\] |
| \[10\times \text{ }M\text{ sin }30{}^\circ 2M\times 5\text{ sin }45{}^\circ \] |
| \[=M\text{ }{{\text{v}}_{2}}\text{ sin }45{}^\circ 2M\text{ }{{\text{v}}_{1}}\text{ sin }30{}^\circ \] |
| \[5-5\sqrt{2}=\frac{{{\text{v}}_{2}}}{\sqrt{2}}-{{\text{v}}_{1}}\] |
| Solving \[{{\text{v}}_{1}}=\frac{17.5}{2.7}\simeq 6.5m/s\] |
| \[{{\text{v}}_{2}}\approx 6.3\,m/s\] |
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