Two masses of $$6$$ and $$2$$ unit, are at positions (6i^-7j^) and (2i^$$ $$+$$ $$5j^-8k^) respectively. The coordinates of the centre of mass are [JIPMER $$2017$$]

Question

Two masses of $$6$$ and $$2$$ unit, are at positions (6i^-7j^) and (2i^$$ $$+$$ $$5j^-8k^) respectively. The coordinates of the centre of mass are [JIPMER $$2017$$]

Infinity Learn · Accepted Answer

Given, masses, $$m1$$ $$=$$ $$6$$ unit and $$m2$$ $$=$$ $$2$$ unitPositions $$=$$ $$6i^-7j^$$ and $$2i^$$ $$+$$ $$5j^-8k^Coordinates$$ of centre of mass are calculated below          $$xCM=m1x1+m2x2m1+m2=6$$×$$6+2$$×$$26+2=36+48=5i^$$         $$yCM=m1y1+m2y2m1+m2=6$$×$$(-7)+2$$×(5)6+2$$                 $$=-42+108=-4j^and$$     $$zCM=m1z1+m2z2m1+m2=6$$×$$(0)+2$$×$$(-8)6+2=-168=-2k^$$∴ Centre of mass lies at $$5i^-4j^-2k^$$.⇒ Coordinates of centre of mass are $$(5$$, $$-4$$, $$-2).

Two masses of 6 and 2 unit, are at positions $(6 \hat{i} - 7 \hat{j})$ and $(2 \hat{i} + 5 \hat{j} - 8 \hat{k})$ respectively. The coordinates of the centre of mass are [JIPMER 2017]

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Two masses of 6 and 2 unit, are at positions (6i^-7j^) and (2i^ + 5j^-8k^) respectively. The coordinates of the centre of mass are [JIPMER 2017]

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Two masses of 6 and 2 unit, are at positions $(6 \hat{i} - 7 \hat{j})$ and $(2 \hat{i} + 5 \hat{j} - 8 \hat{k})$ respectively. The coordinates of the centre of mass are [JIPMER 2017]