question_answer

A bomb of mass \[30kg\]at rest explodes into two pieces of masses \[18\,kg\] and \[12\,kg\]. The velocity of \[18\,kg\]mass is \[6\,m{{s}^{-1}}\]. The kinetic energy of the other mass is [CBSE PMT 2005]

A)                 256 J     

B)                 486 J     

C)                 524 J     

D)                 324 J

Correct Answer: B

Solution :

    According to law of conservation of linear momentum                  \[{{m}_{A}}{{v}_{A}}={{m}_{B}}{{v}_{B}}\]= \[18\times 6=12\times {{v}_{B}}\]Þ \[{{v}_{B}}=9\ m/s\]                 K.E.  of mass 12 kg, \[{{E}_{B}}=\frac{1}{2}{{m}_{B}}v_{B}^{2}\]                   = \[\frac{1}{2}\times 12\times {{(9)}^{2}}=486J\]