# 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 v1 and v2, respectively. The values of v1 and v2 are nearly: (a) 3.2m/s and 12.6m/s (b) 3.2m/s and 6.3m/s (c) 6.5m/s and 3.2 m/s (d) 6.5m/s and 6.3m/s

## Question ID - 51335 | Toppr Answer 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 v1 and v2, respectively. The values of v1 and v2 are nearly: (a) 3.2m/s and 12.6m/s (b) 3.2m/s and 6.3m/s (c) 6.5m/s and 3.2 m/s (d) 6.5m/s and 6.3m/s

3537

Answer Key : (d) -

Apply conservation of linear momentum in X and Y direction for the system then

M(10cos300)+2M(5cos450)=2M(v1cos300)+M(v2cos450)

5 v1+                          … (1)

Also 2M(5sin450)−M(10sin300)=2Mv1sin300−Mv2sin450

5 −5=v1     … (2)

Solving equation (1) and (2)

( +1)v1=5 +10 −5

⇒ v1=6.5m/s, v2=6.3m/s