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 magnitude of position vector of centre of mass of this system will be similar to the magnitude of 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 magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector : (A)  hati-2 hatj+ hatk (B) -3 hati-2 hatj+ hatk (C) -2 hati+2 hatk (D) -2 hati- hatj+2 hatk

Tardigrade Admin · Accepted Answer

rc o m= (m1 r1+m2 r2/m1+m2)=(1( hat i +2 hat j + hat k )+3(-3 hat i -2 hat j + hat k )/1+3) = -2 hat i - hat j + hat k |2 hat i - hat j + hat k |=√(2)2+(1)2+(1)2=√6

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 magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector :

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

$- 3 \hat{i} - 2 \hat{j} + \hat{k}$

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

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

$r_{co m} = \frac{m _{1} r _{1} + m _{2} r _{2}}{m _{1} + m _{2}} = \frac{1 ( i ^ + 2 j ^ + k ^ ) + 3 ( - 3 i ^ - 2 j ^ + k ^ )}{1 + 3}$
$= - 2 \hat{i} - \hat{j} + \hat{k}$
$∣2 \hat{i} - \hat{j} + \hat{k} ∣ = (2)^{2} + (1)^{2} + (1)^{2} = 6$

Q. Two bodies of mass 1kg and 3kg have position vectors i^+2j^​+k^ and −3i^−2j^​+k^ respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector :

i^−2j^​+k^

−3i^−2j^​+k^

−2i^+2k^

−2i^−j^​+2k^