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

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

Tardigrade Admin · Accepted Answer

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

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}{2} + 4 \times \frac{80}{2} + 0}{16} = \frac{30}{2}

Similarly,

y = \frac{30}{2} so, r = x^{2} + y^{2} = 30 c m

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

20 cm

30 cm

40 cm

60 cm

According to figure let A is the origin and co - ordinates of centre of mass be (x, y), then, x=m1​+m2​+m3​+m4​m1​x1​+m2​x2​+m3​x3​+m4​x4​​ =160+2×2​80​+4×2​80​+0​=2​30​ Similarly, y=2​30​so,r=x2+y2​=30cm

Q. Masses $8, 2, 4, 2 k g$ are placed at the corners A, B, C, D respectively of a square ABCD of diagonal $80 c m$ . The distance of centre of mass from A will be