Consider the following mass distribution: 7.2 kg at (4 m, 1 m), 2.3 kg at (0 m, 4.3 m), and 2.5 kg at (4.4 m, 0 m). We need to place a fourth mass of 9.7 kg so that the center of gravity of the four-mass arrangement will be at (0, 0). Find the x coordinate of such a point.

Explanation:

Given:

coordinates of center of mass of the system,

The system comprises of the following masses with their position:

We know the center of mass is given as:

&

Explanation:

m1 = 7.2 kg at (4m, 1m)

m2 = 2.3 kg at (0 m, 4.3 m )

m3 = 2.5 kg at (4.4 m, 0 m)

Let the fourth mass, m4 = 9.7 kg is placed at (x' y') so that the centre of mass is at (0, 0) of the system of masses.

use the formula of centre of mass

Here, xcm, ycm = (0, 0)

21.7 = 28.8 + 11 + 9.7 x'

- 18.1 = 9.7 x'

x' = - 1.87 m

21.7 = 7.2 + 9.89 + 9.7 y'

4.61 = 9.7 y'

y' = 0.475 m

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