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A $30\,kg$ shell is flying at $48\,m/s$ , when it explodes its one part is $18\,kg$ stops while the remaining part flies on. Find the velocity of the latter.

Last updated date: 22nd Jul 2024
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Hint:In order to this question, to know the velocity of the remaining part which is flying, we will first rewrite the given facts and then we will find the mass of the remaining part of the shell. And then we will apply the law of conservation of momentum to find the velocity of the remaining part of the shell.

Complete step by step answer:
We will rewrite facts of the given question-
Mass of the shell, $M = 30\,kg$
Velocity of the shell, $V = 48\,m/s$
After explosion-
Mass of the first part, ${m_1} = 18\,kg$
As its stops, so the velocity of the first part, ${v_1} = 0\,m/s$
So, the mass of remaining part is, ${m_2} = 30\,kg - 18\,kg = 12\,kg$
We have to find the velocity of the remaining part or ${v_2}$
Now, according to the law of conservation of momentum:-
$MV = {m_2}{v_2} \\ \Rightarrow 30 \times 48 = 12{v_2} \\ \Rightarrow {v_2} = \dfrac{{30 \times 48}}{{12}} \\ \therefore {v_2} = 120\,m/s \\$
Hence, the velocity of the required part is $120\,m/s$.

Note:The general law of physics states that in an isolated set of objects, the quantity called momentum, which characterises motion, never changes; that is, the total momentum of a system remains constant.