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  4. 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 upsilon1 and upsilon2, respectively. The values of upsilon1 and upsilon2 are nearly :

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Q. 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 :Physics Question Image

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Solution:

$ M \times10 \cos30^{\circ} +2M \times 5\cos45^{\circ} $
$ = 2M \times V_{1} \cos30^{\circ} + M V_{2} \cos 45^{\circ} $
$ 5\sqrt{3} + 5\sqrt{2} = 2v_{1} \frac{\sqrt{3}}{2} + \frac{v_{2}}{\sqrt{2}} $
$ 10 \times M \sin 30^{\circ} - 2M \times 5\sin 45^{\circ} $
$ = M v_{2} \sin 45^{\circ} - 2M v_{1} \sin 30^{\circ} $
$ 5- 5\sqrt{2} = \frac{v_{2}}{\sqrt{2} } - v_{1} $
Solving $ v_{1} = \frac{17.5 }{2.7 }\simeq 6.5 m/s $
$ v_{2} \approx 6.3 \,m/s$