Question

Two particles of masses 4kg and 2kg are approaching towards each other with acceleration 1 metre per second square into metre per second square if the respectively on a smooth horizontal surface find the acceleration of centre of mass of the system

Answer 1

Answer:

Given:

Mass of the 2 bodies are 4 kg and 2 kg.

They are moving at acceleration of

1 m/s² towards each other.

To Find:

Acceleration of centre of mass

Calculation:

For a system of masses , the acceleration of centre of mass is given as follows :

$acc = \frac{ \Sigma(m_{i}a_{i})}{\Sigma (m_{i})}$

$= > acc. = \frac{(2 \times 2) - (4 \times1) }{(2 + 4)}$

$= > acc. = 0 \: \: m {s}^{ - 2}$

So acceleration of Center of Mass is zero

This can be explained in another way:

• Since gravitational force is an internal force between the masses, hence we can say that centre of mass doesn't move and hence its acceleration is zero.

Answer 2

GIVEN:-

Two particles of masses 4kg and 2kg are approaching towards each other with acceleration 1 metre per second square.

SOLUTION :-

the acceleration of Centre of mass.

acceleration =Σ(mi ai) /Σ(mi)

$\implies$ acceleration=(2×2)-(4×1)/(2+4)

$\implies$ acceleration=4-4/6

$\implies$ acceleration=0/6

$\implies$ acceleration=0m/s².

HENCE,

ACCELERATION OF CENTER OF MASS IS 0m/s².