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A solid sphere of radius R is placed on ...

A solid sphere of radius R is placed on a cube of side 2R. Both are made of same material. Find the distance of their centre of mass fro the interface.

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To find the distance of the center of mass from the interface between a solid sphere and a cube, we will follow these steps: ### Step 1: Identify the dimensions and masses - The radius of the sphere \( R \). - The side length of the cube \( 2R \). - Both objects are made of the same material, so they have the same density \( \rho \). ### Step 2: Calculate the mass of the sphere ...
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Knowledge Check

  • A solid hemisphere and a solid cone have a common base and are made of same material. The centre of mass of the common structure coincides with the centre of the common base. If R is the radius of hemisphere and h is height of the cone, then

    A
    `(h)/(R )=sqrt(3)`
    B
    `(h)/(R )=(1)/sqrt(3)`
    C
    `(h)/(R )=3`
    D
    `(h)/(R )=(1)/(3)`

  • A circular hole of radius r is made in a disk of radius R and of uniform thickness at a distance a from the centre of the disk. The distance of the new centre of mass from the original centre of mass is

    A
    `(aR^(2))/(R^(2)-r^(2))`
    B
    `(ar^(2))/(R^(2)-r^(2))`
    C
    `(a(R^(2)-r^(2)))/(r^(2))`
    D
    `(a(R^(2)-r^(2)))/(R^(2))`

  • A hemispherical cavity of radius R is created in a solid sphere of radius 2R as shown in the figure . Then y -coordinate of the centre of mass of the remaining sphere is

    A
    `Y_("CM")=-R/15`
    B
    `Y_("CM")=-R/40`
    C
    `Y_("CM")=-R/30`
    D
    `Y_("CM")=-R/20`

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