Question 165: Centre of Mass and Rotational Motion

Question

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 u
1
and u
2
, respectively.
The values of u
1
and u
2
are nearly :

Accepted Answer

2MV, cos 30ÃÂ° + Mv
2
cos 45ÃÂ° = 10 M cos 30ÃÂ° + 10 cos 45ÃÂ°
$$ \Rightarrow {v_1}\sqrt 3  + {{{v_2}} \over {\sqrt 2 }} = 5\sqrt 3  + 5\sqrt 2 $$   ...(i)
2MV, sin 30ÃÂ° Ã¢ÂÂ MV
2
sin 45ÃÂ° = Ã¢ÂÂ10 M sin 30ÃÂ° + 10 M sin 45ÃÂ°
$${V_1} - {{{V_2}} \over {\sqrt 2 }} =  - 5 + 5\sqrt 2 $$   ...(ii)
$${V_1} = {{5\left( {\sqrt 3  - 1} \right) + 10\sqrt 2 } \over {\sqrt 3  + 1}} = {{17.5} \over {2.7}} = 6.5\,m/s$$
V
2
= 6.3 m/s

Answer

6.5 m/s and 3.2 m/s

Answer

6.5 m/s and 6.3 m/s

Answer

3.2 m/s and 6.3 m/s

Answer

3.2 m/s and 12.6 m/s

Centre of Mass and Rotational Motion

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 u 1 and u 2 , respectively. The values of u 1 and u 2 are nearly :

Choose the correct answer: