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In planetary motion the areal velocity o...

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 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) = (L)/(2m) rArr (dA)/(dt) prop vr prop omega r^(2)`
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Knowledge Check

  • 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^(@)`

  • Relation between Linear velocity (v) and Angular velocity (omega)

    A
    `v = r omega`
    B
    `omega = v omega`
    C
    `r = v omega`
    D
    `v = omega/r`

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