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Many planets are revolving around the fi...

Many planets are revolving around the fixed sun in circular orbits of different radius `(R)` and difference time period `(T)` To estimate the mass of the sun the orbital radius `(R)` and time period `(T)` of planets were noted. Then `"log"_(10)` T v/s `"log"_(10)R` curve was plotted.
The curve was found to be approximately straight line (as shown in) having y intercept `=6.0` (Neglect the gravitational interaction among the planets) [Take `G = (20)/(3) xx 10^(-11)` in MKS, `pi^(2)= 10`]

The slope of the line should be .

A

`1`

B

`(3)/(2)`

C

`(2)/(3)`

D

`(19)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • If a planet revolves around the sun in a circular orbit of radius a with a speed of revolution T, then (K being a positive constant

    A
    `T = Ka^(2//3)`
    B
    `T = Ka^(3//2)`
    C
    `T = Ka^(2)`
    D
    `T = Ka^(3)`

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    A
    4 T
    B
    T/8
    C
    T/4
    D
    8 T

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    `(T pi)/(2e)`
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