The centre of the mass of \(3\) particles, \(10~\text{kg},\)  \(20~\text{kg},\) and \(30~\text{kg},\) is at \((0,0,0).\) Where should a particle with a mass of \(40~\text{kg}\) be placed so that its combined centre of mass is \((3,3,3)?\)
1. \((0,0,0)\)
2. \((7.5, 7.5, 7.5)\)
3. \((1,2,3)\)
4. \((4,4,4)\)

Four particles of mass \(m_1 = 2m\), \(m_2=4m\), \(m_3 =m \), and \(m_4\) are placed at the four corners of a square. What should be the value of \(m_4\) so that the centre of mass of all the four particles is exactly at the centre of the square?

Three masses are placed on the x-axis: \(300\) g at the origin, \(500\) g at \(x =40\) cm, and \(400\) g at \(x=70\) cm. The distance of the center of mass from the origin is:

Five uniform circular plates, each of diameter \(D\) and mass \(m,\) are laid out in a pattern shown. Using the origin shown, the \(y\text-\text{coordinate}\) of the centre of mass of the ''five–plate'' system will be:

A man '\(A\)', mass \(60\) kg, and another man '\(B\)', mass \(70\) kg, are sitting at the two extremes of a \(2\) m long boat, of mass \(70\) kg, standing still in the water as shown. They come to the middle of the boat. (Neglect friction). How far does the boat move on the water during the process?

The coordinates of the centre of mass of a uniform plate of shape as shown in the figure are:

The mass per unit length of a non-uniform rod of length \(L\) is given by \(\mu =λx^{2}\) where \(\lambda\) is a constant and \(x\) is the distance from one end of the rod. The distance between the centre of mass of the rod and this end is: