question_answer

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

Correct Answer: A

Solution :

 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 \[M=1+2+0.7=3.7\]