Question: Masses 8, 2, 4, 2 kg are placed at the corners A, B, C, D respectively of a square ABCD of diagonal ...

Question

Masses 8, 2, 4, 2 kg are placed at the corners A, B, C, D respectively of a square ABCD of diagonal 80 cm. The distance of centre of mass from A will be:

Answer 1

Solution

According to figure let A is the origin and co-ordinates of centre of mass be (x,y), then,

$x = \frac{m_{1}x_{1} + m_{2}x_{2} + m_{3}x_{3} + m_{4}x_{4}}{m_{1} + m_{2} + m_{3} + m_{4}} = \frac{0 + 2 \times \frac{80}{\sqrt{2}} + 4 \times \frac{80}{\sqrt{2}} + 0}{16} = \frac{30}{\sqrt{2}}$

Similarly $y = \frac{30}{\sqrt{2}}$

So, $r = \sqrt{x^{2} + y^{2}} = 30$ cm