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The ratio of the dimensions of Planck's ...

The ratio of the dimensions of Planck's constant and that of moment of inertia has the dimensions of

A

angular momentum

B

time

C

velocity

D

frequency

Text Solution

Verified by Experts

The correct Answer is:
D
We know that, energy of an emitted particle,
`" "E=hvrArrh=(E)/(nu)`
Planck's constant
`h=(["ML"^(2)"T"^(-2)])/("T"^(-1))=["ML"^(2)"T"^(-1)]" "…(i) `
and moment of inertia,
`I=mr^(2)rArrI=["ML"^(2)]" "...(ii)`
On dividing Eq. (i) by Eq. (ii), we get
`(h)/(I)=[("ML"^(2)"T"^(-1))/("ML"^(2))]=["T"^(-1)]=(1)/("T")`
i.e., `" "(h)/(I)=["T"^(-1)]`= frequency of a particle.
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Knowledge Check

  • The ratio of the dimension of Planck's constant and that of moment of inertia is the dimension of

    A
    Frequency
    B
    Velocity
    C
    Angular momentum
    D
    Time

  • The ratio of the dimensions of plank's constant and that of the moment of inertia is the dimension of

    A
    frequency
    B
    velocity
    C
    angular momention
    D
    time

  • The dimensions of Planck's constant are

    A
    `kg m^(2) s^(-1)`
    B
    `kg m s^(-2)`
    C
    `kg^(2) m^(2) s^(-1)`
    D
    `kg m^(2) s^(-2)`

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