Four particles with masses 2kg, 4kg, 2kg, and $x$ kg are placed at the vertices of a square. We need to find the value of $x$ such that the center of gravity of the system lies at the center $O$ of the square.

1. Problem Description

Four particles with masses 2kg, 4kg, 2kg, and $x$ kg are placed at the vertices of a square. We need to find the value of $x$ such that the center of gravity of the system lies at the center $O$ of the square.

2. Solution Steps

For the center of gravity to be at the center of the square, the system must be balanced. This means that the masses opposite each other must be equal.

In other words, the sum of masses on one diagonal equals the sum of masses on the other diagonal.

$2 kg + 4 kg = 2 kg + x kg$

$6 kg = 2 kg + x kg$

$x kg = 6 kg - 2 kg$

$x = 4$

3. Final Answer

4 kg