Question

The product of the total mass of a system and the velocity of the center of mass is:
1. the angular momentum of the system
2. the linear momentum of the system
3. the total energy of the system
4. the potential energy of the system

Answer 1

Correct Answer - Option 2 : the linear momentum of the system

The correct answer is option 2) i.e. the linear momentum of the system

CONCEPT:

• Linear momentum: Momentum is defined as the impact due to a moving object.
  • Linear momentum, p = mv

Where m is the mass of the object and v is the velocity of the object.

EXPLANATION:

Let us consider a system of particles with each particle having a mass  m and velocity v.

If p is the linear momentum od each particle, p = mv

Total linear momentum, Σp = Σmv = Σm . Σv = M.v_com

Where M is the sum of mass of all particles, and v_com is the velocity of the centre of mass.

The vector addition of velocities will give a net velocity with respect to the centre of mass.

Hence, the linear momentum of a system = product of the total mass of a system and the velocity of the centre of mass