Question

A shell at rest at the origin explodes into three fragments of masses 1 kg, 2 kg and m kg. The 2 kg and 1 kg pieces fly off with speeds of 12 m/s along $x-$ axis and 16 m/s along $y-$ axis respectively. If the m kg piece flies off with a speed of 40 m/s, the total mass of the shell must be

• A. 3.7kg
• B. 4kg
• C. 4.5 kg
• D. 5kg

Answer 1

Answer: (A)

From principle of conservation of momentum, if no external force acts upon a system of two or more bodies, then the total momentum of the system remains constant. Resolving the momentum components, we have
$p_x-p_m\cos \theta =0$
$p_y-p_m\sin \theta =0$
$\therefore$ $p_m=\sqrt{p_x^2+p_y^2}$
$m\times 40=\sqrt{{(2\times 12)}^2+{(1\times 16)}^2}$
$\Rightarrow$ $m\times 40=29$
$\Rightarrow$ $m=0.7$
Hence, total mass of the shell
$M=1+2+0.7=3.7$