Question 11: Centre of Mass and Rotational Motion

Question

A bomb of mass 20 kg at rest explodes into two pieces of masses 12 kg and 8 kg . If the velocity of 8 kg mass is $6 \mathrm{~ms}^{-1}$, then the kinetic energy of the other mass is:

Accepted Answer

Let the two fragments have masses $m_1=8$ kg and $m_2=12$ kg, with $v_1=6$ m/s. By conservation of momentum (initial momentum zero):
Ã¢ÂÂ¢ $m_1v_1 + m_2v_2 = 0$
$\displaystyle 8\cdot6 + 12\,v_2 = 0$
$\displaystyle 48 + 12\,v_2 = 0$
$\displaystyle v_2 = -4$ m/s
(The minus sign just means it moves opposite to the 8 kg piece; its speed is 4 m/s.)
Now its kinetic energy is
$ 	ext{KE}_2 = 	frac12\,m_2\,v_2^2             = 	frac12\cdot12\cdot(4)^2             = 6\cdot16             = 96	ext{ J}. $
Answer: 96 J.

Answer

144 J

Answer

64 J

Answer

86 J

Answer

96 J

Centre of Mass and Rotational Motion

A bomb of mass 20 kg at rest explodes into two pieces of masses 12 kg and 8 kg . If the velocity of 8 kg mass is 6 \mathrm{~ms}^{-1}, then the kinetic energy of the other mass is:

Choose the correct answer: