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  4. 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

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Q. 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

Jharkhand CECEJharkhand CECE 2010

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 $

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