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Three planets of same density and with r...

Three planets of same density and with radii `R_1,R_2` and `R_3` such that `R_1=2R_2=3R_3` have gravitation fields strength on planets are `v_1,v_2,v_3`, respectively. Then :

A

`g_1//g_2=1//2`

B

`g_1//g_3=3`

C

`v_1//v_2=2`

D

`v_1//v_3 =1//3`

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
`v=sqrt(2qR)=sqrt((2GM)/R)=sqrt((2G)/R(rho4/3piR^3))=sqrt((8piGP)/3)R`
Therefore , `rArr v_1/v_2=R_1/R_2 =2 , g_1/g_2=3 , g_1/g_3=R_1/R_3=3 , v_1/v_3=R_1/R_3=3`
`g=(GM)/R^2 =G/R^2 (rho 4/3 piR^3) =(5piGP)/3 R`
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