Four particle of masses $$m1$$ $$=$$ $$2m$$, $$m2$$ $$=$$ $$4$$ m, $$m3$$ $$=$$ m and $$m4$$ are placed at four corners of a square. What should be the value of $$m4$$ so that the centres of mass of all the four particles are exactly at the centre of the square?

Question

Four particle of masses $$m1$$ $$=$$ $$2m$$, $$m2$$ $$=$$ $$4$$ m, $$m3$$ $$=$$ m and $$m4$$ are placed at four corners of a square. What should be the value of $$m4$$ so that the centres of mass of all the four particles are exactly at the centre of the square?

Infinity Learn · Accepted Answer

Let side of square is a.xcm $$=$$ $$a2$$ $$=$$ $$m1$$×$$0+m2$$×$$a+m3$$×$$a+m4$$×$$0m1+m2+m3+m4solve$$ to get $$m4$$ $$=$$ $$3$$ mycm $$=$$ $$a2$$ $$=$$ $$m1$$×$$0+m2$$×$$0+m3$$×$$a+m4$$×$$am1+m2+m3+m4solve$$ to get $$m4$$ $$=$$ $$5mThey$$ are contradicting, so it is not possible to have centre of mass at the centre of square.

Four particle of masses $m_{1} = 2 m, m_{2} = 4 m, m_{3} = m and m_{4}$ are placed at four corners of a square. What should be the value of $m_{4}$ so that the centres of mass of all the four particles are exactly at the centre of the square?

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Four particle of masses m1 = 2m, m2 = 4 m, m3 = m and m4 are placed at four corners of a square. What should be the value of m4 so that the centres of mass of all the four particles are exactly at the centre of the square?

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Ready to Test Your Skills?

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Four particle of masses $m_{1} = 2 m, m_{2} = 4 m, m_{3} = m and m_{4}$ are placed at four corners of a square. What should be the value of $m_{4}$ so that the centres of mass of all the four particles are exactly at the centre of the square?