Question

Two particles, of masses $M$ and $2M$, moving, as shown, with speeds of $10m/s$ and $5m/s$, 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 :

• 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

Answer 1

Answer: (C)

$M\times 10\cos 30^{\circ }+2M\times 5\cos 45^{\circ }$
$=2M\times V_1\cos 30^{\circ }+M{V}_2\cos 45^{\circ }$
$5\sqrt{3}+5\sqrt{2}=2v_1\frac{\sqrt{3}}{2}+\frac{v_2}{\sqrt{2}}$
$10\times M\sin 30^{\circ }-2M\times 5\sin 45^{\circ }$
$=M{v}_2\sin 45^{\circ }-2M{v}_1\sin 30^{\circ }$
$5-5\sqrt{2}=\frac{v_2}{\sqrt{2}}-v_1$
Solving $v_1=\frac{17.5}{2.7}\simeq 6.5m/s$
$v_2\approx 6.3m/s$