Question

A 9-kg object is at rest. Suddenly, it explodes and breaks into two pieces. The mass of one piece is 6 kg and the other is a 3-kg piece. Which one of the following statements concerning these two pieces is correct?
a. The speed of the 6-kg piece will be one eighth that of the 3-kg piece.
b. The speed of the 3-kg piece will be one fourth that of the 6-kg piece.
c. The speed of the 6-kg piece will be one forth that of the 3-kg piece.
d. The speed of the 3-kg piece will be one half that of the 6-kg piece.
e. The speed of the 6-kg piece will be one half that of the 3-kg piece.

Answer 1

Answer:

e).

Explanation:

Assuming no external forces acting during the instant of the explosion, total momentum must be conserved.

As the object was initially at rest, the initial momentum is zero, which means that after the explosion, total momentum must add to zero too.

Let's call m₁ = 3 kg-piece and m₂= 6 kg-piece.

⇒ m₁*v₁ + m₂*v₂ = 0

⇒ 3kg* v₁ = -6kg*v₂

⇒ 6/3 = 2 = v₁/v₂ ⇒ v₂/v₁ = 1/2 (in magnitude)

v₂ (being the speed of the 6-kg piece) = 1/2 * v₁ (speed of thr 3-kg piece).

So, we conclude in that  the statement e) is the one that is true.