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A shell at rest at the origin explodes into three fragments of masses \( 1 \mathrm{~kg}, 2 \mathrm{~kg} \) and \( m \mathrm{~kg} \). The \( 1 \mathrm{~kg} \) and \( 2 \mathrm{~kg} \) pieces fly off with speeds of \( 5 \mathrm{~ms}^{-1} \) along \( x \)-axis and \( 6 \mathrm{~ms}^{-1} \) along \( y \)-axis respectively. If the \( m \mathrm{~kg} \) piece flies off with a speed of \( 6.5 \mathrm{~ms}^{-1} \), the total mass of the shell must be
[Kerala PET 2007]
(a) \( 4 \mathrm{~kg} \)
(b) \( 5 \mathrm{~kg} \)
(c) \( 3.5 \mathrm{~kg} \)
(d) \( 4.5 \mathrm{~kg} \)
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