Question

Two particle, of masses $M$ and $2M$, moving, ash 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 $v_1$ and $v_2$, respectively. the values of $v_1$ and $v_2$ are nearly:

• A. $3.2m/s$ and $6.3m/s$
• B. $3.2m/s$ and $12.6m/s$
• C. $6.5m/s$ and $6.3m/s$
• D. $6.5m/s$ and $3.2m/s$

Answer 1

The correct option is C $6.5m/s$ and $6.3m/s$

$M\times 10cos{30}^0+2M\times 5cos{45}^0$
$=2M\times v_{1}cos{30}^0+M{v}_{2}cos{45}^0$
$5\sqrt{3}+5\sqrt{2}=2v_1\frac{\sqrt{3}}{2}+\frac{v_2}{\sqrt{2}}$
$10\times Msin{30}^0-2M\times 5sin{45}^0$
$=M{v}_{2}sin{45}^0-2M{v}_{1}sin{30}^0$
$5-5\sqrt{2}=\frac{v_2}{\sqrt{2}}-v_1$
solving $v_1=\frac{17.5}{2.7}\approx 6.5m/s$
$v_2\approx 6.3m/s$