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If all the particlke of a system lie in X-Y plane is it necessary that the centre of mass be in X-Y plane?

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Yes
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If all the particle of a system lie n a cube is it necessary that the cente of mas be in the cube?

The centre of mass is defined as vecR=1/Msum_im_ivecr_i . Suppose we define centre of charge as vecR_c=1/Qsum_iq_Ivecr_i where q_i represents the ith charge placed at vecr_i and Q is the total charge of the sytem a. Can a centre of charge of a two charge system be outside the line segment joining the charges? b. If all the charges of a system are in X-Y plane? c. ILf all the charges f a system lie in a cube, is it necessary that the centre of charge be in the cube?

Knowledge Check

  • Two rods of equal lengths(l) and equal mass M are kept along x and y axis respectively such that their centre of mass lie at origin. The moment of inertia about an line y = x, is

    A
    `(ml^(2))/(3)`
    B
    `(ml^(2))/(4)`
    C
    `(ml^(2))/(12)`
    D
    `(ml^(2))/(6)`

  • Four point mass, each of mass m are connected at a corner of a square of side 'a' , by massless rods as shown in the figure. x and y axis are in the plane of the system and z axis is perpendicualr to the plane and passing through the centre of the square.

    A
    Moment of inertia of the system about `x` axis is `I_(x)=ma^(2)`
    B
    Moment of inertia of the system about `y` axis is `I_(y)=ma^(2)`
    C
    Moment of inertia of the systeme about the diagonal axis `AA' ` is `I_(AA')=ma^(2)`
    D
    Moment of inertia of the system about `z` axis is `I_(2)=ma^(2)`

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