A 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 `5ms^(-1)` along x-axis and `6ms^(-1)` along y-axis respectively. If the m kg piece flies off with a speed of `6.5ms^(-1)`, the total mass of the shell must be

Options

A. A)4 kg
B. B)5 kg
C. C)3.5 kg
D. D)4.5 kg

Answer

B

Explanation

We can realise the situation as shown in figure. Let the directio of mass m makes angle `theta` with the z-axis.
Resolve momentum 6.5 m along x and y-axis and equate.

Therefore,
`6.5mcostheta=5xx1`
and `6.5msintheta=6xx2`
or `(6.5m)^(2)=(5)^(2)+(12)^(2)=(13)^(2)`
or `m=(13)/(6.5)=2kg`
Therefore, total mass of the shell.
`=1+2+2=5kg`