Question

An object at rest in space suddenly explodes into three parts of same mass. The momentum of the two parts are $2p\hat{i}\ and p\hat{j}$. The momentum of the third part(a) will have a magnitude p√3(b) will have a magnitude p√5(c) will have a magnitude p(d) will have a magnitude 2p.

Answer 1

Answer:b) will have a magnitude p√5 is the correct answer of the given question.

Explanation:

An object at rest in space.

It suddenly explodes into three parts of same mass.

The momentum of the two parts are 2pi and pj.

To find

The momentum of the the third part.

We will use the law of conservation of momentum in this question.

The law of conservation of momentum states that the total momentum of a body before collision is equal to the total momentum of body after collision.

It works only if no external force is applied to it.

Thus in short the total momentum is conserved.

So

According to the principle of conservation of momentum,

p+2pi+pj=0

p=-2pi-pj

p= √(-2p) ^2+(p) ^2

p= √5p^2

p=√5p

Thus magnitude of momentum is √5p of the third point. (Answer)

Answer 2

Answer:

total momentum =2i^ +pj^

magnitude =√(2p)²+(p)²=√5p²=√5p

Explanation:

the 3rd part will have momentum of p√5