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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

1 Answer - 5876 Votes

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



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