# Formula For Velocity of Centre of Mass

## Formula for Velolcity of Centre of Mass

The center of mass is the location of particles within a system where the system's total mass can be considered to be concentrated. When the system of particles moves, the center of mass moves along with it. The center of the mass velocity equation is the sum of each particle's momentum (mass times velocity) divided by the system's total mass.

Where,

m = mass in kilograms (kg)

v = velocity in meters per second (m/s)

### Examples For Velocity of Centre of Mass

Problem 1: The velocities of three particles of masses 20g, 30g and 50 are 10i,10j and 10k respectively. The velocity of the centre of mass of the three particle us

a. 2i+3j+5k

b. 10(i+j+k)

c. 20i+30j+5k

d. 2i+30j+50k

Solution: correct option is a

Problem 2: A ball kept in a closed container moves in it making collision with the walls. The container is on a smooth surface. The velocity of the centre of mass of

(a) the ball remains fixed.

(b) ball relative to container remains the same.

(c) container remains fixed.

(d) ball container and ball remains fixed.

Solution: Correct option is (d)

Since the container is closed, the collisions made by the ball with the walls of a container will not affect the mass of container and in turn, there is no change in velocity of the centre of mass.

Problem 3: Two objects P and Q initially at rest move towards each other under a mutual force of attraction. At the instant when the velocity of P is V and that of Q is 2v the velocity of the centre of mass of the system is

(a) 2v

(b)   3v

(c)  1.5v

(d) Zero

Solution: Correct option is e.

Since they move due to the mutual interaction between two objects so, the centre of mass remains the same and its velocity is zero.

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