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A large number of particles are placed a...

A large number of particles are placed around the origin, each at a distance R from the origin. The distance of the center of mass of the system from the origin is

A

`r=d`

B

`r le d`

C

`r ge d`

D

`r=0`

Text Solution

Verified by Experts

The correct Answer is:
B
We can visualise a hypothetical circle of radius d on the X-Y plane. All the particles must lie on this circle. Now assume a situation when all the particles are kept at the same point on the circumference of the circle then centre of mass of the system will also lie at the same location hence in this case r=d. But when we distribute particles to different point on the circumference of the circle then centre of mass lies inside the circle hence in these cases `rltd`. We can also distribute particles on this circle in such a way that centre of mass lies at the origin. Option (b) is correct.
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Knowledge Check

  • All the particles of a body are situated at a distance R from the origin. The distance of the centre of mass of the body from the origin is

    A
    `=R`
    B
    `leR`
    C
    `gtR`
    D
    `geR`

  • All the particles of a body situated at distance d from the origin. The distance of the center of mass of the body from the origin is

    A
    `= d`
    B
    `le d`
    C
    `gt d`
    D
    `ge d`

  • The distance of the B(6,6) from the origin is:

    A
    ` sqrt(53)` units
    B
    ` sqrt(41) ` units
    C
    ` sqrt( 72)` units
    D
    `sqrt(145)` units
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