question_answer

A shell at rest at the origin explodes into three fragments of masses 1kg, 2 kg and m kg. The 1kg and 2 kg pieces fly off with speeds of\[5\text{ }m{{s}^{-1}}\] along x-axis and\[6\text{ }m{{s}^{-1}}\]along y-axis respectively. If the m kg piece flies off with a speed of\[6.5\text{ }m{{s}^{-1}},\]the total mass of the shell must be

A)  4kg                                       

B)  5kg                       

C)  3.5 kg                  

D)         4.5 kg

E)  5.5kg

Correct Answer: B

Solution :

We can realise the situation as shown in figure. Let the direction of mass m makes angle\[\theta \]with the\[z-\]axis. Resolve momentum 6.5m along\[x\]and y-axis and equate. Therefore, \[6.5m\text{ cos}\,\theta =5\times 1\] and        \[6.5\,m\,\sin \theta =6\,\times 2\] or            \[{{(6.5\text{ }m)}^{2}}={{(5)}^{2}}+{{(12)}^{2}}={{(13)}^{2}}\] or            \[m=\frac{13}{6.5}=2\,kg\] Therefore, total mass of the shell \[=1+2+2=5\text{ }kg\]