Question 227: Centre of Mass and Rotational Motion

Question

A bomb of mass $$16kg$$ at rest explodes into two pieces of masses $$4$$ $$kg$$ and $$12$$ $$kg.$$ The velocity of the $$12$$ $$kg$$ mass is $$4\,\,m{s^{ - 1}}.$$ The kinetic energy of the other mass is

Accepted Answer

Here linear momentum is conserved as no external force is acting on the bomb.
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 linear momentum
$$0 = {m_2}{v_2} - {m_1}{v_1}$$
$$\Rightarrow {v_1} = {{12 	imes 14} \over 4} = 12\,m{s^{ - 1}}$$
$$	herefore$$ $$K.E{_1} = {1 \over 2}{m_1}v_1^2 = {1 \over 2} 	imes 4 	imes 144 = 288\,J$$

Answer

$$144$$ $$J$$

Answer

$$288$$ $$J$$

Answer

$$192$$ $$J$$

Answer

$$96$$ $$J$$

Centre of Mass and Rotational Motion

A bomb of mass $16kg at rest explodes into two pieces of masses 4 kg and 12 kg. The velocity of the 12 kg mass is 4\,\,m{s^{ - 1}}.$ The kinetic energy of the other mass is

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