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 $g_{2}$ respectively, then

Q. Two planets of same density, have radii

R_{1}

and

R_{2}

such that

R_{1} = 2 R_{2}

. If the escape velocity on the planets are

v_{1}

and

v_{2}

respectively. Then ratio

\frac{v_{2}}{v_{1}}

is equal to

The radii of two planets are respectively $R_{1}$ and $R_{2}$ and their densities are respectively $ρ_{1} a n d ρ_{2}$ . The ratio of the accelerations due to gravity at their surface is

Join BYJU'S Learning Program

Three planets of same density have radii R1,R2 and R3 such that R1=2R2=3R3The gravitational field at their respective surfaces are g1,g2 and g3 and escape velocities from their surfaces are v1,v2 and v3 then

The correct options are A g1/g3=3 C g1/g2=2 D v1/v3=3Earth surface gravity g=GMR2=G(4/3πR3ρ)R2 where ρ= density of earth. So g∝REscape velocity ve=√2gR=√2GMRR2=√2G(4/3πR3ρ)RAs ρ is constant so ve∝RThus, g1/g2=R1/R2=2 ; g1/g3=R1/R3=3v1/v2=R1/R2=2;v1/v3=R1/R3=3

Three planets of same density have radii $R_{1}, R_{2}$ and $R_{3}$ such that $R_{1} = 2 R_{2} = 3 R_{3}$ The gravitational field at their respective surfaces are $g_{1}, g_{2}$ and $g_{3}$ and escape velocities from their surfaces are $v_{1}, v_{2}$ and $v_{3}$ then