Two particles of mass 2 kg and 1 kg are placed at points (1,-2) and (-4,3). Where should a third particle of mass 5 kg be placed so that centre of mass of three particle system lies at origin ?

Question

Two particles of mass 2 kg and 1 kg are placed at points (1,-2) and (-4,3). Where should a third particle of mass 5 kg be placed so that centre of mass of three particle system lies at origin ? (A) ((1/5), (2/5)) (B) ((2/5), (1/5)) (C) ((3/5), (4/5)) (D) ((-2/5), (-1/5))

Tardigrade Admin · Accepted Answer

X cm =( m 1 x 1+ m 2 x 2+ m 3 x 3/ m 1+ m 2+ m 3) ⇒ O =((2)(1)+(1)(-4)+5 x 3/2+1+5) ⇒ 5 x 1+2-4 x 1=(2/5) Y cm =( m 1 y 1+ m 2 y 2+ m 3 y 3/ m 1+ m 2+ m 3) ⇒ O =(2(-2)+1(3)+ m 3 y 3/2+1+ m 3) ⇒ -4+3+5 y 3=0 ⇒ 5 y 3=1 y 3=(1/5)

Q. Two particles of mass $2 k g$ and $1 k g$ are placed at points $(1, - 2)$ and $(- 4, 3)$ . Where should a third particle of mass $5 k g$ be placed so that centre of mass of three particle system lies at origin ?

$(\frac{1}{5}, \frac{2}{5})$

$(\frac{2}{5}, \frac{1}{5})$

$(\frac{3}{5}, \frac{4}{5})$

$(\frac{- 2}{5}, \frac{- 1}{5})$

Q. Two particles of mass 2kg and 1kg are placed at points (1,−2) and (−4,3). Where should a third particle of mass 5kg be placed so that centre of mass of three particle system lies at origin ?

(51​,52​)

(52​,51​)

(53​,54​)

(5−2​,5−1​)

Xcm​=m1​+m2​+m3​m1​x1​+m2​x2​+m3​x3​​ ⇒O=2+1+5(2)(1)+(1)(−4)+5x3​​ ⇒5x1​+2−4 x1​=52​ Ycm​=m1​+m2​+m3​m1​y1​+m2​y2​+m3​y3​​ ⇒O=2+1+m3​2(−2)+1(3)+m3​y3​​ ⇒−4+3+5y3​=0 ⇒5y3​=1 y3​=51​

Q. Two particles of mass $2 k g$ and $1 k g$ are placed at points $(1, - 2)$ and $(- 4, 3)$ . Where should a third particle of mass $5 k g$ be placed so that centre of mass of three particle system lies at origin ?

$(\frac{1}{5}, \frac{2}{5})$

$(\frac{2}{5}, \frac{1}{5})$

$(\frac{3}{5}, \frac{4}{5})$

$(\frac{- 2}{5}, \frac{- 1}{5})$