The following formula represents the principle of conservation of ______.
\(m_1u_1+m_2u_2=m_1v_1+m_2v_2\), where \(m_1, m_2\) are masses of two bodies, \(u_1, u_2\) are initial velocities and \(v_1, v_2\) are final velocities.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Linear momentum
The linear momentum of a body is mass × velocity (\(p=mv\)). The formula says that the total momentum of the two bodies before they interact (\(m_1u_1+m_2u_2\)) equals their total momentum after (\(m_1v_1+m_2v_2\)), which is the principle of conservation of linear momentum. It holds when no external force acts, as in a collision or the recoil of a gun.
Why the other options are incorrect
Option (1) Angular momentum — Incorrect. Angular momentum is about rotation (\(I\omega\)); its conservation uses moment of inertia and angular velocity.
Option (3) Energy — Incorrect. Kinetic energy would use \(\frac{1}{2}mv^2\), with the squares of the velocities.
Option (4) Velocity — Incorrect. Velocity is not conserved; the velocities change from u to v in the formula itself.