Q. A shell of rest at the origin explodes into three fragments of masses 1 kg, 2 kg and $m$ kg. The 1 kg and 2 kg pieces fly off with speed of ${5\ ms}^{- 1}$ along $x$-axis and ${6\ ms}^{- 1}$ along $y$-axis respectively. If the $m$ kg piece flies off with 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) We can realize the situation as shown in figure. Let the direction of mass $m$ makes angle $\theta$ with the $z$-axis. Resolve momentum 6.5$m$ along x and y –axis and equate.
[image:5_image247.emf]
Therefore, $6.5m\cos{\theta = 5 \times 1}$
and $6.5\ m\sin\theta = 6 \times 2$
$or\ \ (6.5m)^{2} = (5)^{2} + (12)^{2} = (13)^{2}$
$or\ \ m = \frac{13}{6.5} = 2\ kg$
therefore, total mass of the shell
$= 1 + 2 + 2 = 5$ kg
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.