Home
Class 11
PHYSICS
If the radius of the earth be increased ...

If the radius of the earth be increased by a factor of `5`, by what factor its density be changed to keep the value of `g` of the same?

A

`1//25`

B

`1//5`

C

`1//sqrt(5)`

D

`5`

Text Solution

Verified by Experts

The correct Answer is:
b
`g=(GM)/(R^(2))=g=(Grhoxx4/3piR^(3))/(R^(2))`
`g=4/3piGRrho...(1)`
`g'=4/3piG(5R)eho'...(2)`
given that `g=g'`, so `rho'=rho/5`
Promotional Banner

Similar Questions

Explore conceptually related problems

If the radius of the earth were incresed by a factor of 3, by what factor would its density to be changed to keep 'g' the same ?

Keeping mass unchanged if radius of the earth increases by a factor 4, then by which factor density must have to be changed so that the value of g remains same ?

If the radius of the earth were increased by a factor of 2 keeping the mass constant, by what factor would its density have to be changed to keep g the same?

If the energy of the photon is increased by a factor of 4 , then its momentum

If the distance between two bodies is increased by a factor of 5, (i) by what factor will the gravitational force change if the masses are kept consant ? (ii) by what factor will the mass of one of them have to be altered, keeping the other mass the same, to maintain the same gravitational force between the two bodies.?

If the distance between two masses is increased by a factor of 5, by what factor would the mass of one of them have to be altered to maintain the same gravitational force? Would this be an increase or decrease in the mass?

If the distance between two masses is increased by a factor of 4, by what factor would the mass of one of them have to be altered to maintain the same gravitational force?