Physics · Work, Energy And Power · NEET
Linear momentum is a vector, and a vector is conserved only when each of its components is conserved. In a 2D (oblique) collision the bodies move off at angles, so a single line cannot describe all the motion. We set up an x-axis and a y-axis, then write conservation of momentum for x and for y as two separate scalar equations. NCERT states this directly: momentum being a vector implies three equations for x, y and z; choosing the collision plane as the x-y plane makes the z-equation trivial, leaving two useful equations.
Only if the collision is elastic. Momentum (x and y components) is always conserved in every collision, elastic or inelastic. Kinetic energy is conserved as an extra condition only when the collision is elastic. So for an elastic oblique collision you get three equations total: momentum along x, momentum along y, and kinetic energy. For an inelastic oblique collision you keep only the two momentum equations.
For a typical elastic 2D collision, the knowns are the masses and the initial speed. The unknowns are the two final speeds and the two scattering angles, so four unknowns. Conservation gives you only three equations (x-momentum, y-momentum, kinetic energy). That is one equation short, so at least one angle must be given in the problem to make it solvable. This is why NEET 2D collision questions almost always tell you one angle.
An oblique collision is one where the line of motion of at least one body after the collision is not along the original line of approach. The bodies scatter at angles to the initial direction, so the whole event needs a plane (two dimensions) to describe, not a single line. Games like billiards and carrom are everyday oblique collisions.
An explosion is just a collision run backwards in time. One body at rest breaks into fragments. Since no external force acts, total momentum stays zero, so the vector sum of all fragment momenta is zero. You still resolve into x and y components and set each component sum to zero. NEET's 2019 fragment question is exactly this idea.
A particle of mass 5m at rest suddenly breaks on its own into three fragments. Two fragments of mass m each move along mutually perpendicular directions with speed v each. The energy released during the process is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Total linear momentum is always conserved, and you apply it separately to the x-direction and the y-direction. Kinetic energy is conserved only if the collision is elastic.
Because conservation gives three equations for elastic collisions but there are four unknowns (two final speeds and two angles). Giving one angle removes the shortfall so the problem becomes solvable.
Yes. NEET tests it mostly as explosion or fragment problems (a body at rest breaking into pieces moving at angles), where you resolve momenta into components. The 2019 paper had one such question.
If both angles are zero the motion is along a single line, and the 2D equations collapse back into the standard one-dimensional collision equations.
Usually take the x-axis along the initial velocity of the incoming body. Then the incoming momentum has only an x-component and zero y-component, which makes the y-momentum equation start from zero and stays simple.
