question_answer

A bomb of 12 kg explodes into two pieces of masses 4 kg  and 8 kg. The velocity of 8kg mass is 6 m/sec. The kinetic energy of the other mass is                                         [MNR 1985; CPMT 1991; Manipal MEE 1995; Pb. PET 2004]

A)                 48 J        

B)                 32 J

C)                 24 J        

D)                 288 J

Correct Answer: D

Solution :

                    As the initial momentum of bomb was zero, therefore after explosion two parts should possess numerically equal momentum  i.e. \[{{m}_{A}}{{v}_{A}}={{m}_{B}}{{v}_{B}}\]Þ \[4\times {{v}_{A}}=8\times 6\]Þ \[{{v}_{A}}=12\ m/s\]                 \ Kinetic energy of other mass A, = \[\frac{1}{2}{{m}_{A}}v_{A}^{2}\]                 = \[\frac{1}{2}\times 4\times {{(12)}^{2}}\]= 288 J.