A bomb of mass 9 kg explodes into two pieces of masses 3 kg and 6 kg. The velocity of mass 3 kg is `16 m s^(-1)`. The kinetic energy of mass 6 kg in joule is 

Options

A. 96
B. 384
C. 192
D. 768

Answer

C

Explanation

According to the law of conservation of momentum
`0 = m_1 v_1 + m_2v_2 " or " m_2v_2 = -m_1v_1`
Taking only the magnitude,
`m_2v_2 = m_1v_1`
`:. K_2 = 1/2 m_2v_2^2 = 1/2 (m_2^2 v_2^2)/(m_2) = (m_1^2 v_1^2)/(2m_2) " (Using (i))"`
`= ((3)^2 xx (16)^2)/(2 xx 6) = 192 J`