Two planets have the same average density but their radii are R1 and R2. If acceleration due to gravity on these planets be g1 and g2, then :

Question

Two planets have the same average density but their radii are R1 and R2. If acceleration due to gravity on these planets be g1 and g2, then : (A)  (g1/g2)=(R13/R23)  (B)  (g1/g2)=(R12/R22)  (C)  (g1/g2)=(R2/R1)  (D)  (g1/g2)=(R1/R2)

Tardigrade Admin · Accepted Answer

Acceleration due to gravity g=(GM/R2) =(GVd/R2)=G((4/3)π R3d/R2) 8=(4/3)π GdR ...(1) Both the planet have same average density . Hence, g propto R Therefore, (g1/g2)=(R1/R2)

Q. Two planets have the same average density but their radii are $R_{1}$ and $R_{2} .$ If acceleration due to gravity on these planets be $g_{1}$ and $g_{2},$ then :

$\frac{g 1}{g 2} = \frac{R _{1}^{3}}{R _{2}^{3}}$

$\frac{g 1}{g 2} = \frac{R _{1}^{2}}{R _{2}^{2}}$

$\frac{g 1}{g 2} = \frac{R _{2}}{R _{1}}$

$\frac{g 1}{g 2} = \frac{R _{1}}{R _{2}}$

Acceleration due to gravity $g = \frac{GM}{R ^{2}}$ $= \frac{G V d}{R ^{2}} = G \frac{\frac{4}{3} π R ^{3} d}{R ^{2}}$ $8 = \frac{4}{3} π G d R$ ...(1) Both the planet have same average density . Hence, $g \propto R$ Therefore, $\frac{g _{1}}{g _{2}} = \frac{R _{1}}{R _{2}}$

Q. Two planets have the same average density but their radii are R1​ and R2​. If acceleration due to gravity on these planets be g1​ and g2​, then :

g2g1​=R23​R13​​

g2g1​=R22​R12​​

g2g1​=R1​R2​​

g2g1​=R2​R1​​