An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 ms^-1 and the second part of mass 2 Kg moves with 8 ms^-1 speed. If the third part files off with 4 ms^-1 speed, then its mass is : 

5 kg

Conservation of Momentum : \(\vec{P_1} + \vec{P_2} + \vec{P_3} = 0 \)

\(\sqrt{(m_1v_1)^2 + (m_2v_2)^2} = m_3v_3 \)

\(m_1 = 1 kg ; m_2 = 2 kg ; v_1 = 12 m/s ; v_2 = 8 m/s ; v_3 = 4 m/s \)

\(\sqrt{(1×12)^2 + (2×8)^2}\) = m₃(4)

⇒ \(m_3 = 5 kg\)