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Question

All particles are situated at a distance $$R$$ from the origin. The distance of centre of mass of the body from the origin will be


A
More than R
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B
Less than R
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C
Equal to R
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D
At the origin
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Solution

The correct option is D At the origin
$$\because \quad all\quad particles\quad at\quad a\quad distance\quad at\quad R\\ center\quad of\quad mass=\frac { { m }_{ 1 }{ X }_{ 1 }+{ m }_{ 2 }{ X }_{ 2 }+{ m }_{ 3 }{ X }_{ 3 }+\cdots +{ m }_{ n }{ X }_{ n } }{ \left( { m }_{ 1 }{ +m }_{ 2 }+{ m }_{ 3 }+\cdots +{ m }_{ n } \right)  } \\ \because \quad { X }_{ 1 }={ X }_{ 2 }={ X }_{ 3 }={ X }_{ 4 }=R\\ So\quad the\quad center\quad of\quad mass\quad now\quad lies\quad at\quad the\quad center\quad of\quad the\quad circle\quad where\quad all\quad the\quad particles\quad lie.\\ \Rightarrow So\quad at\quad the\quad origin\\ $$


Physics

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