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Calculate the mass of sum if the mean ra...

Calculate the mass of sum if the mean radius of the earth's orbit is `1.5xx10^(8)km` and `G=6.67xx10^(-11)Nxxm^(2)//kg^(2)`

A

`M=2xx10^(30)kg`

B

`M=3xx10^(30)`

C

`M=2xx10^(15)kg`

D

`M=3xx10^(15)kg`

Text Solution

Verified by Experts

The correct Answer is:
A
In case of orbital motion as `v=sqrt(((GM)/(r)))` so `T=(2pir)/(v)=2pirsqrt((r)/(GM)),` i.e., `M=(4pi^(2)r^(3))/(GT^(2))`
`M=(4xxpi^(2)xx(1.5xx10^(11))^(3))/(6.67xx10^(-11)xx(3.15xx10^(7))^(2))` [as `T=1` year `=3.15xx10^(7)s]` i.e., `M=2xx10^(30)kg`
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