Two bodies of mass 1 kg and 3 kg have position vectors hat i +2 hat j + hat k and -3 hat i -2 hat j + hat k , respectively. The centre of mass of this system has a position vector:

Question

Two bodies of mass 1 kg and 3 kg have position vectors hat i +2 hat j + hat k and -3 hat i -2 hat j + hat k , respectively. The centre of mass of this system has a position vector: (A) -2 hati- hatj+ hatk (B) 2 hati- hatj-2 hatk (C) - hati+ hatj+ hatk (D) -2 hati+ hatk

Tardigrade Admin · Accepted Answer

The position vector of centre of mass vecr= vecr=(m1 vecr1+m2 vecr2/m1+m2) ltbrtgt =(1( hati+2 hatj+ hatk)+3(-3 hati-2 hatj+ hatk)/1+3) =(1/4)(-8 hati-4 hatj+4 hatk) =-2 hati- hatj+ hatk

Q. Two bodies of mass $1 k g$ and $3 k g$ have position vectors $\hat{i} + 2 \hat{j} + \hat{k}$ and $- 3 \hat{i} - 2 \hat{j} + \hat{k}$ , respectively. The centre of mass of this system has a position vector:

$- 2 \hat{i} - \hat{j} + \hat{k}$

$2 \hat{i} - \hat{j} - 2 \hat{k}$

$- \hat{i} + \hat{j} + \hat{k}$

$- 2 \hat{i} + \hat{k}$

The position vector of centre of mass
$r = r = \frac{m _{1} r _{1} + m _{2} r _{2}}{m _{1} + m _{2}}$
ltbrtgt $= \frac{1 ( i ^ + 2 j ^ + k ^ ) + 3 ( - 3 i ^ - 2 j ^ + k ^ )}{1 + 3}$
$= \frac{1}{4} (- 8 \hat{i} - 4 \hat{j} + 4 \hat{k})$
$= - 2 \hat{i} - \hat{j} + \hat{k}$

Q. Two bodies of mass 1kg and 3kg have position vectors i^+2j^​+k^ and −3i^−2j^​+k^, respectively. The centre of mass of this system has a position vector:

−2i^−j^​+k^

2i^−j^​−2k^

−i^+j^​+k^

−2i^+k^