Two particles of masses M and 2 M are moving with speeds of 10 m s - 1 and 5 m s - 1 , as shown in the figure. They collide at the origin and after that they move along the indicated directions with speeds v 1 and v 2 , respectively. The values of v 1 and v 2 are, nearly

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Aicharya · Accepted Answer

From conservation of linear momentum,
Along $x$ -axis:

${10Mcos30}^{0} + 5 (2M c o s 45^{0}) = M v_{1} c o s 30^{0} + 2 M v_{2} c o s 45^{0}$
$10 M \frac{\sqrt{3}}{2} + 10 M \frac{1}{\sqrt{2}} = M \frac{\sqrt{3}}{2} v_{1} + 2 M v_{2} \frac{1}{\sqrt{2}}$
$\frac{\sqrt{3}}{2} v_{1} + \sqrt{2} v_{2} = 5 (\sqrt{3} + \sqrt{2})$ … (1)
Along $y$ -axis:
$- 10 M \frac{1}{2} + 10 M \frac{1}{\sqrt{2}} = M v_{1} \frac{1}{2} - 2 M v_{2} \frac{1}{\sqrt{2}}$
$\frac{v_{1}}{2} - \sqrt{2} v_{2} = 5 (\sqrt{2} - 1)$ … (2)
From equations (1) and (2)
$v_{1} (\frac{\sqrt{3}}{2} + \frac{1}{2}) = 5 (\sqrt{3} + \sqrt{2}) + 5 (\sqrt{2} - 1)$
$v_{1} = 13.02 m / s$
$v_{2} = \frac{5 \sqrt{3} + 5 \sqrt{2} - 13.02 \times \frac{\sqrt{3}}{2}}{\sqrt{2}}$
$= 19.72 m s^{- 1}$

Two particles of masses M and 2 M are moving with speeds of 10 m s - 1 and 5 m s - 1 , as shown in the…

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