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  4. A body of mass M at rest explodes into three pieces, in the ratio of masses 1: 1: 2. Two smaller pieces fly off perpendicular to each other with velocities of 30 ms -1 and 40 ms -1 respectively. The velocity of the third piece will be :

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Q. A body of mass $M$ at rest explodes into three pieces, in the ratio of masses $1: 1: 2$. Two smaller pieces fly off perpendicular to each other with velocities of $30\, ms ^{-1}$ and $40 \,ms ^{-1}$ respectively. The velocity of the third piece will be :

JEE MainJEE Main 2022Laws of Motion

Solution:

Mass of pieces by $\frac{M}{4}, \frac{M}{4}, \frac{M}{2}$
conserving momentum
$\overrightarrow{ P }_{1}+\overrightarrow{ P }_{2}+\overrightarrow{ P }_{3}=0$
$\overline{ P }_{3}=-\left(\overline{ P }_{1}+\overline{ P }_{2}\right)$
As $\overline{ P }_{1} \& \overline{ P }_{2}$ are perpendicular
so $P _{3}=\sqrt{ P _{1}^{2}+ P _{2}^{2}}$
$P _{3}=(50) \frac{ M }{4}$
$\& P _{3}=\frac{ M }{2} V$
so $v=25$