Question : A bomb at rest explodes into 3 parts of the same mass. The momentum of 2 parts are -2i and pj. The linear momentum of the third part will have a magnitude of
a) p
b) √3p
c) √(3p)
d) Zero
Doubt by Saif
Solution :
P1 = -2i
P2 = pj
P2 = pj
P3 = ?
As per the Law of conservation of Linear Momentum.
Linear Momentum before the explosion = Linear Momentum after the explosion
Pi = Pf
0 = P1+P2+P3
P3 = -(P1+P2)
P3 = -(-2i+pj)
P3 = 2i-pj
Now, magnitude of linear momentum of the third part
0 = P1+P2+P3
P3 = -(P1+P2)
P3 = -(-2i+pj)
P3 = 2i-pj
Now, magnitude of linear momentum of the third part
|P3| = √[(2)2+(p)2].
|P3| = √[4+p2]
OR
P3 = √[4+p2]
OR
P3 = √[4+p2]
No option are matching, it means there is something wrong with the question. But don't worry you should focus on the method.