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If the orbital velocity of a planet is g...

If the orbital velocity of a planet is given by `v = G^(a) M^(b) R^(c )` then

A

`a = (1)/(2), b = (1)/(2), c = (1)/(2)`

B

`a = (1)/(2), b = (1)/(2), c = - (1)/(2)`

C

`a = (1)/(2), b = - (1)/(2), c = (1)/(2)`

D

`a = (1)/(3), b = - (1)/(3), c = - (1)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
(2) `v = G^(a) M^(b) R^(c )`
`LT^(-1) = [M^(-1) L^(3) T^(-2)]^(a) [M]^(b) [L]^(c )`
`M^(0) L^(1) T^(-1) = M^(-a + b) L^(3a + c) T^(-2a)`
Comparing power of `M, L` and `T`
`-a + b = 0`
`3 a + c = 1`
`-2a = - 1 implies a = (1)/(2), b = (1)/(2), c = -(1)/(2)`
OR
Orbital velocity `v = sqrt((GM)/(R )), v = G^(a) M^(b) R^(c )`
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Knowledge Check

  • If orbit velocity of planet is given by v = G^(a)M^(b)R^(c) , then

    A
    `a = (1)/(3),b=(1)/(3),c=-(1)/(3)`
    B
    `a=(1)/(3),b=(1)/(2),c=-(1)/(2)`
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    `a=(1)/(2), b=-(1)/(2),c=(1)/(2)`
    D
    `a=(1)/(2),b=-(1)/(2),c=-(1)/(2)`

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  • The orbital velocity of the planet will be minimum at :

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