Question

Three equal masses each of 50 g, are placed at the corners of a right angled isosceles triangle whose two equal sides are 5 cm each. The position of the centre of mass of the system is ____________.

Options

• x = 5 cm, y = 5 cm

• `"x" = 5/3  "cm", "y" = 5  "cm"`

• `"x" = 5/3  "cm", "y" = 5/2  "cm"`

• `"x" = 5/3  "cm", "y" = 5/3  "cm"`

Answer 1

Three equal masses each of 50 g, are placed at the corners of a right angled isosceles triangle whose two equal sides are 5 cm each. The position of the centre of mass of the system is `"x" = 5/3  "cm", "y" = 5/3  "cm"`.

Explanation:

\[X_{\text{C.M}}=\frac{\sum\limits_{i=1}^{3}m_ix_i}{\sum\limits_{i=1}^{3}m_i}\]

`= (0 xx 50 + 50 xx 5 + 0 xx 50)/(50 + 50 + 50)`

`= 250/150`

` = 5/3  "cm"`

\[Y_{\text{CM}}=\frac{\sum\limits_{i=1}^{3}m_ix_i}{\sum\limits_{i=1}^{3}m_i}\]

`= (0 xx 50 + 0 xx 50 + 5 xx 50)/(50 + 50 + 50)`

`= 250/150`

` = 5/3  "cm"`