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

• A. 20 cm
• B. 30 cm
• C. 40 cm
• D. 60 cm

Answer 1

Answer: (B)

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}}=30cm \, $