A bomb at rest explodes into three parts of same mass. The momentum of two parts is Find the magnitude of momentum of third point. - Wired Faculty

Laws Of Motion

Question

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A bomb at rest explodes into three parts of same mass. The momentum of two parts is $italic minus italic 2 p i with italic hat on top italic space a n d italic space p j with italic hat on top italic.$ Find the magnitude of momentum of third point.

Solution

Let $straight P with rightwards arrow on top$ be the momentum of third point.
According to law of conservation of linear momentum,
$straight P with rightwards arrow on top space minus space 2 straight p straight i with hat on top space plus space straight p space straight j with hat on top space equals space 0$
$rightwards double arrow$ $P with italic rightwards arrow on top italic space italic equals italic space italic 2 p italic space i with italic hat on top italic space italic minus italic space p j with italic hat on top$
i.e., $straight P with rightwards arrow on top space equals space square root of left parenthesis 2 straight p right parenthesis squared plus left parenthesis straight p right parenthesis squared end root space equals space left parenthesis square root of 5 right parenthesis straight p$ , is the required magnitude of momentum of the third point.