Question

A stationary shell breaks into three fragments. The momentum of two of the fragments in Peach and
move at 60° to each other. The momentum of the third fragment is-
please answer

Answer 1

Answer:

$\sqrt{3}P$

Explanation:

The resultant of the two momentums will be just like the resultant of two forces making an angle $\theta$

$P'=\sqrt{P^2+P^2+2\times P\times P\cos\theta}$

$\implies P'=\sqrt{2P^2+2P^2\cos60^\circ}$

$\implies P'=\sqrt{2P^2+2P^2\cos60^\circ}$

$\implies P'=\sqrt{2P^2+2P^2\times\frac{1}{2}}$

$\implies P'=\sqrt{3P^2}$

$\implies P'=\sqrt{3}P$

From the principle of conservation of linear momentum, the momentum of the third fragment will be just opposite to the resultant momentum of the two fragment

Thus, the momentum of the third fracment = -$\sqrt{3}P$

The magnitude of the momentum = $\sqrt{3}P$

Hope this helps.