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The uniform solid sphere shown in the fi...

The uniform solid sphere shown in the figure has a spherical hole in it. Find the position of its centre of mass.

Text Solution

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The correct Answer is:
A, B, C
`x_(CM)=(V_1x_1-V_2x_2)/(V_1-V_2)`
`=((4/3piR^3)(0)-((4pia^3)/(3))(b))/((4/3piR^3)-4((pia^3)/(3)))`
`=(-a^3b)/(R^3-a^3)`
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Knowledge Check

  • Inside a uniform sphere of density rho there is a spherical cavity whose centre is at a distance l from the centre of the sphere. Find the strength of the gravitational field inside the cavity.

    A
    `E=(-2)/3 piGrhol`
    B
    `E=(-4)/3piGrhol`
    C
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    D
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  • A solid sphere of radius R is rolled by a force F acting at the topo of the sphere as shown in the figure. There is no slipping and initially sphere is in the rest position, then (CM= centre of mass)

    A
    Work done by force F when the centre of mass move a distance S is 2 FS
    B
    speed of the CM when CM moves a distance S is `sqrt((20)/(7)(FS)/(M))`
    C
    work done by the Force F when CM move a distance S is FS
    D
    speed of the CM when CM moves a distance S is `sqrt((6)/(5)(FS)/(M))`

  • 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
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    B
    `Y_("CM")=-R/40`
    C
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    D
    `Y_("CM")=-R/20`

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