11. An object of mass 3m, initially at rest, explodes breaking into two fragment

Question

11. An object of mass 3m, initially at rest, explodes breaking into two fragments of mass m and 2m. respectively. Which one of the following statements concerning the fragments after the explosion is true? A) They will fly off at right angles. B) They will fly of in the same direction. C) The smaller fragment will have twice the speed of the larger fragment. D) The larger fragment will have twice the speed of the smaller fragment. E) The smaller fragment will have four times the speed of the larger fragment.

Explanation / Answer

First let's suppose that the all the energy during collision is converted to kinetic energy(in reality it does not- sound, light, heat, etc may be produced although at negligible amount).because if we don't there is no way to find any answer. KE= 0.5mv^2 KE=(m^2)*(v^2)/(m*2) KE=((mv)^2)/2m KE= P^2/2m .... P is the momentum P^2=KE*2m Since momentum is conserved during collision, PA-PB=0 PA=PB PA^2=PB^2 KE of A *2m of A=KE of B *2m of B (KE of A)/(KE of B)=(m of B / m of A) KE of A = (m of B / m of A) *KE of B..... eqn 1 From the supposition we made at the beginning, KE of A + KE of B = Q (m of B / m of A) *KE of B+KE of B =Q KE of B ((m of B / m of A) +1)=Q KE of B = Q/((m of B / m of A)).... eqn 2 use eqn 1 and eqn 2 to calculate calculate KE of A The second question is just about putting the values. A gets 20% and B gets 80%. It takes long time to type that all on to computer. C) The smaller fragment will have twice the speed of the larger fragment

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