Centre of Mass 3 Question 12

15. A particle of mass m is projected from the ground with an initial speed u0 at an angle α with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u0. The angle that the composite system makes with the horizontal immediately after the collision is (2013 Adv.)

(a) π4

(b) π4+α

(c) π4α

(d) π2

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Answer:

Correct Answer: 15. (a)

Solution:

  1. From momentum conservation equation, we have,

mmu0cosαu022gHj^^i^pi=pfm(u0cosα)i^+m(u022gH)j^=(2m)vH=u02sin2α2g

From Eqs. (i) and (ii)

v=u0cosα2i^+u0cosα2j^

Since both components of v are equal. Therefore, it is making 45 with horizontal.



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