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Find the minimum radius for a planet of ...

Find the minimum radius for a planet of mean density `rho` and temperature `T` which can detain oxygen in its atmosphere. (`M_(0)=`Molecular weight of Oxygen and `G=`Universal Gravitational constant)

A

`sqrt((7)/(8)(RT)/(GM_(0)rhopi))`

B

`sqrt((9)/(8)(RT)/(GM_(0)rhopi))`

C

`sqrt((15)/(9)(RT)/(GM_(0)rhopi))`

D

`sqrt((15)/(8)(RT)/(GM_(0)rhopi))`

Text Solution

AI Generated Solution

To find the minimum radius \( R \) for a planet of mean density \( \rho \) and temperature \( T \) that can detain oxygen in its atmosphere, we will follow these steps: ### Step 1: Understand the Concept of Escape Velocity The escape velocity \( v_e \) is the minimum velocity needed for an object to escape the gravitational pull of a planet. It is given by the formula: \[ v_e = \sqrt{\frac{2GM}{R}} \] where \( G \) is the universal gravitational constant, \( M \) is the mass of the planet, and \( R \) is the radius of the planet. ...
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