Question

A bullet of mass X, moving with a velocity V, strikes a wooden block of mass Z and
gets embedded. If the block is free to move, its velocity after impact will be.
A. $\dfrac{X}{X+Z}V$
B. $\dfrac{X+Z}{Z}V$
C. $\dfrac{X}{X-Z}V$
D. $\dfrac{X+Z}{X}V$

Answer 1

Hint: Collisions of molecules are versatile, for instance Rutherford backscattering. A helpful exceptional instance of versatile collision is the point at which the two bodies have equivalent mass, in which case they will basically trade their momenta.

Complete step-by-step answer:

Initial momentum = $XV+0={{P}_{i}}$
Final momentum =${{V}_{f}}+(Z+X)={{P}_{f}}$
Applying linear momentum conservation on (bullet f block) system :
${{P}_{i}}={{P}_{f}}$
$XV={{V}_{f}}(Z+X)$
⇒${{V}_{f}}=\left( \dfrac{X}{X+Z}V \right)$

The correct answer is A.

Additional Information:
In a collision, the velocity change is constantly registered by taking away the underlying velocity esteem from the last velocity esteem. In the event when an object is moving one way before a collision and bounce back or by one way or another alters course, at that point its velocity after the collision has the other way as before.

A versatile collision is an experience between two bodies wherein the absolute kinetic energy of the two bodies continues as before. In a perfect, totally flexible collision, there is no net transformation of kinetic energy into different structures, for example, warmth, commotion, or potential energy.

During the collision of little items, kinetic energy is first changed over to potential energy related with a terrible force between the particles (when the particles move against this force, for example the point between the force and the relative velocity is uncaring), at that point this potential energy is changed over back to kinetic energy (when the particles move with this force, for example the point between the force and the relative velocity is intense).

The particles—as particular from iotas—of a gas or fluid once in a while experience entirely versatile collisions in light of the fact that kinetic energy is traded between the atoms' translational motion and their inward degrees of opportunity with every collision.

Note: At any moment, a large portion of the collisions are, to a shifting degree, inelastic collisions (the pair has less kinetic energy in their translational motions after the collision than previously), and half could be depicted as "super-versatile" (having more kinetic energy after the collision than previously).