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Give the location of the centre of mass ...

Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body ?

Text Solution

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The geometrical centre of each. No, the CM may lie outside the body, as in case of a ring, a hollow sphere, a hollow cylinder, a hollow cube etc.
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Knowledge Check

  • Statement : Position of centre of mass of a body is independent of the shape and size of the body. Statement II: The centre of mass of a body may be in a position where there is no mass.

    A
    Statement I is true, statement II is true, statement II is a correct explanation for statement I.
    B
    Statement I is true, statement II true, statement II is not a correct explanation for statement I.
    C
    Statement I is true, statement II is false.
    D
    Statement I is false, statement II is true.
  • Statement I : The mass of a body cannot be considered to be concentrated at the centre of mass of the body for the purpose of computing its moment of inertia. Statement II : For then the moment of inertia of every body about an axis passing through its centre of mass would be zero.

    A
    Statement I is true, statement II is true , statement II is a correct explanation for statement I.
    B
    Statement I is true, statement II is true , statement II is not a correct explanation for statement I.
    C
    Statement I is true, statement II is false.
    D
    Statement I is false, statement II is true.
  • Two bodies of masses m_(1) and m_(2) are separated by a distance R. The distance of the centre of mass of the bodies from the mass m_(1) is

    A
    `(m_(2)R)/(m_(1)+m_(2))`
    B
    `(m_(1)R)/(m_(1)+m_(2))`
    C
    `(m_(1)m_(2))/(m_(1)+m_(2))R`
    D
    `(m_(1)+m_(2))/(m_(1))R`
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