The density of a newly discovered planet...

The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth `R_(e )`, the radius of the planet would be

`2R_(e )`

`4R_(e )`

`(1)/(4)R_(e )`

`(1)/(2)R_(e )`

Text Solution

Verified by Experts

The correct Answer is:

From equation of acceleration due to gravity.
`g_(e )=(GM_(e ))/(R_(e )^(2))=(G(4//3)piR_(e )^(3))/(R_(e )^(2))rho_(e )`
`g_(e )prop R_(e )rho_(e )`
Acceleration due to gravity of planet `g_(p) prop R_(p)rho_(p)`
`:. R_(e )rho_(p) rArr R_(e )rho_(e )=R_(p)2rho_(e ) rArr R_(p)=(1)/(2)r_(e )`

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The density of a newly discovered planet is twice that of the earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth be R, then radius of the planet would be

4 R

`(R )/(2)`

`(R )/(4)`

2 R

The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R , the radius of the planet would be

`2R`

`4R`

`1/4R`

`1/2R`

Acceleration due to gravity at surface of a planet is equal to that at surface of earth and density is 1.5 times that of earth. If radius is R. radius of planet is

`3/2 R`

`2/3 R`

`9/4 R`

`4/9` R