Three particles of masses 1kg, 2kg and 3kg are acted upon by forces (i^+2j^),(2j^+3k^) and (k^+3i^) newton respectively. The angle made by the acceleration of centre of mass with X-axis is (in cos−1)

a¯CM=F¯net∑m=2i3+23J+23K=axi^+ayj^+azk^Angle made by a¯CM with X−axis=cos−1axaCM=cos−113

Three particles of masses 1kg, 2kg and 3kg are acted upon by forces (i^+2j^),(2j^+3k^) and (k^+3i^) newton respectively. The angle made by the acceleration of centre of mass with X-axis is (in cos−1)

a¯CM=F¯net∑m=2i3+23J+23K=axi^+ayj^+azk^Angle made by a¯CM with X−axis=cos−1axaCM=cos−113

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Three particles of masses 1kg, 2kg and 3kg are acted upon by forces $(\hat{i} + 2 \hat{j}), (2 \hat{j} + 3 \hat{k})$ and $(\hat{k} + 3 \hat{i})$ newton respectively. The angle made by the acceleration of centre of mass with X-axis is $(i n \cos^{- 1})$

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$\frac{1}{\sqrt{2}}$

$\frac{\sqrt{3}}{2}$

$\frac{1}{2}$

$\frac{1}{\sqrt{3}}$

answer is D.

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${\bar{a}}_{C M} = \frac{{\bar{F}}_{n e t}}{\sum m} = \frac{2 i}{3} + \frac{2}{3} J + \frac{2}{3} K = a_{x} \hat{i} + a_{y} \hat{j} + a_{z} \hat{k}$

Angle made by ${\bar{a}}_{C M} w i t h X - a x i s = \cos^{- 1} \frac{a_{x}}{|a_{C M}|} = \cos^{- 1} \frac{1}{\sqrt{3}}$

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Three particles of masses 1kg, 2kg and 3kg are acted upon by forces (i^+2j^),(2j^+3k^) and (k^+3i^) newton respectively. The angle made by the acceleration of centre of mass with X-axis is (in cos−1)

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Three particles of masses 1kg, 2kg and 3kg are acted upon by forces $(\hat{i} + 2 \hat{j}), (2 \hat{j} + 3 \hat{k})$ and $(\hat{k} + 3 \hat{i})$ newton respectively. The angle made by the acceleration of centre of mass with X-axis is $(i n \cos^{- 1})$