Q. A shell at rest at the origin explodes into three fragments of masses $1\ kg,\ 2kg$ and $m\ kg$. The $1\ kg$ and $2\ kg$ pieces fly off with speeds off $5ms^{- 1}$ along $x$-axis and $6ms^{- 1}$ along $y$-axis respectively. If the $m\ kg$ piece files off with a speed of $6.5\ ms^{- 1}$, the total mass of the shell must be
A) $4\ kg$
B) $5\ kg$
C) $3.5\ kg$
D) $4.5\ kg$
Explanation
(b) Resolve momentum $6.5\ m$ along $x$ and $y$ axes and equate
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$\therefore 6.5\ m\cos\theta = 5 \times 1$
and $6.5\ m\sin\theta = 6 \times 2$
$\Rightarrow (6.5\ m)^{2} = (5)^{2} + (12)^{2}$
$\Rightarrow 6.5m = 13 \Rightarrow m = 2\ kg$
$\therefore$ Total mass $= 1 + 2 + 2 = 5kg$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.