Question

A 6kg mass collides with a body at rest. After the collision, they travel together with a velocity one third the velocity of 6kg mass. The mass of the second body is-
A.6 kg
B.3 kg
C.12 kg
D.18 kg

Answer 1

The law of conservation of momentum may be deduced from Newton's law of action and reaction, which says that every force has an equal and opposite reciprocating force. Moving charged particles can exert pressures on one other in non-opposite directions in specific conditions. Despite this, the particles' and electromagnetic fields' combined momentum is preserved. We use this concept here,

Complete answer:
One of the most well-known principles in physics is the conservation of momentum. The conservation of momentum principle states that a system's overall momentum is always conserved. The law of conservation of momentum says that unless an external force is introduced, the total momentum of two or more bodies operating on each other in an isolated system remains constant. As a result, neither the creation nor the destruction of momentum is possible. The idea of momentum conservation is a direct result of Newton's third law of motion.
Velocities in one dimension, along a line running through the bodies, can be used to simulate a head-on elastic collision between two bodies. If the velocities are and ${{u}_{2}}$ before the impact and ${{v}_{1}}$ and ${{v}_{2}}$ thereafter, the equations for momentum and kinetic energy conservation are as follows:
${{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}={{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}$
That is ${{P}_{initial}}={{P}_{final}}$
From the given question we can deduce it as
${{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}=({{m}_{1}}+{{m}_{2}})v$
Now given that after the collision, they travel together with a velocity one third the velocity of 6kg mass hence $\dfrac{u}{3}=v$
Hence
$6u+0m=(6+m)\dfrac{u}{3}$
0 represents the u value which is in rest.
Hence we get $\Rightarrow m=12kg$

Hence option c is correct.

Note:
A collision that is elastic is one in which no kinetic energy is converted to heat or another kind of energy. When particles do not touch each other, such as in atomic or nuclear scattering, where electric repulsion keeps the objects away, perfectly elastic collisions can occur. A completely elastic collision can also be seen as a slingshot motion of a satellite around a planet.