Question

A spherical shell at 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 speeds of $12m{s}^{-1}$ along the x-axis and 8 $m{s}^{-1}$ along the y-axis respectively. If the 'm' kg piece flies off with a speed of 40 $m{s}^{-1}$ , the total mass of the shell must be

• A. 3.5 kg
• B. 4.0 kg
• C. 4.5 kg
• D. 5.0 kg

Answer 1

The correct option is A 3.5 kg

From the principle of conservation it follows that the momentum of m kg piece has a magnitude.
$P_3=\sqrt{(12{)}^2+(16{)}^2}=20kgm{s}^{-1}$
$\therefore m=\frac{20kgm{s}^{-1}}{40m{s}^{-1}}=0.5kg$
$\therefore$ Total mass of the shell = 1 + 2 + 0.5 = 3.5 kg. Hence the correct choice is (a).