ge and gp denote the acceleration due to gravity on the surface of the earth and another planet whose mass and radius are twice to that of the earth, then :

Question

ge and gp denote the acceleration due to gravity on the surface of the earth and another planet whose mass and radius are twice to that of the earth, then : (A) gp=(ge/2) (B) gp=ge (C) gp=2 ge (D) gp=(ge/√2)

Tardigrade Admin · Accepted Answer

Acceleration due to gravity is given by g=(G M/R2) where G is gravitational constant. For earth: ge=(G Me/Re2) For planet: gp=(G Mp/Rp2) Therefore, (ge/gp)=(G Me / Re2/G Mp / Rp2) or (ge/gp)=(Me/Mp) × (Rp2/Re2) ...(i) Given, Mp=2 Me, Rp=2 Re Putting the values in the Eq. (i), we obtain (ge/gp) =(Me/2 Me) × ((2 Re2)/Re2) =(1/2) × (4/1) =2 ∴ gp =(ge/2)

Q. $g_{e}$ and $g_{p}$ denote the acceleration due to gravity on the surface of the earth and another planet whose mass and radius are twice to that of the earth, then :

$g_{p} = \frac{g _{e}}{2}$

$g_{p} = g_{e}$

$g_{p} = 2 g_{e}$

$g_{p} = \frac{g _{e}}{2}$

Q. ge​ and gp​ denote the acceleration due to gravity on the surface of the earth and another planet whose mass and radius are twice to that of the earth, then :

gp​=2ge​​

gp​=ge​

gp​=2ge​

gp​=2​ge​​

Q. $g_{e}$ and $g_{p}$ denote the acceleration due to gravity on the surface of the earth and another planet whose mass and radius are twice to that of the earth, then :

$g_{p} = \frac{g _{e}}{2}$

$g_{p} = g_{e}$

$g_{p} = 2 g_{e}$

$g_{p} = \frac{g _{e}}{2}$