An explosion blows a rock into three parts. Two parts go off at right angles to each other. Thes...

An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, \( 1 \mathrm{~kg} \) first part moving with a velocity of \( 12 \mathrm{~ms}^{-1} \) and \( 2 \mathrm{~kg} \) second part moving with a velocity of \( 8 \mathrm{~ms}^{-1} \). If the third part flies off with a velocity of \( 4 \mathrm{~ms}^{-1} \), its mass would be
[CBSE PMT 2009; Similar NEET 2013]
(a) \( 5 \mathrm{~kg} \)
(b) \( 7 \mathrm{~kg} \)
(c) \( 17 \mathrm{~kg} \)
(d) \( 3 \mathrm{~kg} \)