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In planetary motion the areal velocity o...

In planetary motion the areal velocity of position vector of a planet depends of angular velocity `(omega)` and the distance of the planet from sun (r). If so the correct relation for areal velocity is

A

`(dA)/(dt) prop omega r`

B

`(dA)/(dt) prop omega^2 r`

C

`(dA)/(dt) prop omega r^2`

D

`(dA)/(dt) prop sqrt(omega r)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(dA)/(dt)propvrrArr(dA)/(dt)propomegar^2`
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Knowledge Check

  • In planetary motion the areal velocity of possition vector of a planet depends of angular velocity (omega) and the distance of the planet from sun (r). If so the correct relation for areal velocity is

    A
    `(dA)/(dt) prop omegar`
    B
    `(dA)/(dt) prop omega^(2)r`
    C
    `(dA)/(dt) prop omega r^(2)`
    D
    `(dA)/(dt) prop sqrt(omegar)`

  • The escape velocity for a body projected from a planet depends on

    A
    mass of the body
    B
    angle of projection
    C
    mass of the planet
    D
    radius of the body

  • In a uniform circular motion , the velocity, position vector and angular velocity are

    A
    parallel to each other
    B
    mutually prependicular to each other
    C
    they are co-planer
    D
    the angle between them is `45^(@)`