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4-1.Newton's Laws of Motion
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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 ............... $\,ms ^{-1}$
A$15$
B$25$
C$35$
D$50$
(JEE MAIN-2022)
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 $\overline{ P }_{1} \,and \,\overline{ P }_{2}$ are perpendicular
so $P _{3}=\sqrt{ P _{1}^{2}+ P _{2}^{2}}$
$P _{3}=(50) \frac{ M }{4}$
$ and \,P _{3}=\frac{ M }{2} v$
so $v =25$
conserving momentum
$\overrightarrow{ P }_{1}+\overrightarrow{ P }_{2}+\overrightarrow{ P }_{3}=0$
$\overline{ P }_{3}=-\left(\overline{ P }_{1}+\overline{ P }_{2}\right)$
As $\overline{ P }_{1} \,and \,\overline{ P }_{2}$ are perpendicular
so $P _{3}=\sqrt{ P _{1}^{2}+ P _{2}^{2}}$
$P _{3}=(50) \frac{ M }{4}$
$ and \,P _{3}=\frac{ M }{2} v$
so $v =25$
Standard 11
Physics
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