A bomb of mass 16 kg at rest explodes into two pieces of masses 4 kg and 12 kg. velolcity of 12 kg m

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5.Work, Energy, Power and Collision

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A bomb of mass $16\ kg$ at rest explodes into two pieces of masses $4\ kg$ and $12\ kg.$ The velolcity of the $12\ kg$ mass is $4$ $ms^{-1}$. The kinetic energy of the other mass is .............. $\mathrm{J}$

A

$96$

B

$144$

C

$288$

D

$192$

(AIEEE-2006)

Solution

Let the velocity and mass of $4\;kg$ piece be $v_1$ and $m_1$ and that of $12\;kg$ piece be $v_2$ and $m_2$

Applying conservation of liner momentum

$m_2$$v_2$=$m_1$$v_1$=$ \Rightarrow = \frac{{12 \times 4}}{4} = 12$ $m{s^{ – 1}}$

$\therefore \,\,K.E{._1} = \frac{1}{2}{m_1}v_1^2 = \frac{1}{2} \times 4 \times 144 = 288\,J$

Standard 11

Physics

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