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A solid hemisphere and a solid cone have...

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)`

Text Solution

Verified by Experts

The correct Answer is:
C
We have `(1)/(2)Mv^(2)=(1)/(2)kl^(2)`
`v=sqrt((k)/(M))l`
Maximum momentum `=Mv=Msqrt((k)/(M))l=sqrt(Mk)l`
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Knowledge Check

  • A hemisphere and a solid cone have a common base. The center of mass of common structure coincides with the common base. If R is the radius of hemisphere and h is the height of the cone, then h//R will be

    A
    `sqrt(3)`
    B
    `3`
    C
    `(1)/(sqrt(3))`
    D
    `(1)/(3)`

  • The centre of mass of a solid cone along the line form the center of the base to the vertex is at

    A
    One-fourth of the height
    B
    One-third of the height
    C
    One-fifth of the height
    D
    None of these

  • A uniform solid right circular cone of base radius R is joined to a uniform solid hemisphere of radius R and of the same density, as shown. The centre of mass of the composite solid lies at the centre of base of the cone. The height of the cone is

    A
    `1.5R`
    B
    `sqrt(3)R`
    C
    `3R`
    D
    `2sqrt(3)R`

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