1.

Three planets of same density and with radiiR_1,R_2 and R_3such that R_1=2R_2=3R_3have gravitation fields strength on planets arev_1,v_2,v_3, respectively. Then :

Answer»

`g_1//g_2=1//2`
`g_1//g_3=3`
`v_1//v_2=2`
`v_1//v_3 =1//3`

Solution :`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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