Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g', then

Question

Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g', then (A)  g' = g/9 (B) g' =27 g (C) g' =9 g (D) g' =3 g

Tardigrade Admin · Accepted Answer

g= ( GM/r2 ) and g' = ( GM' /r2) [ M' = 3M ] (g'/ g ) = ( 3M/M) ⇒ g' =3g .

Q. Imagine a new planet having the same density as that of earth but it is $3$ times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is $g$ and that on the surface of the new planet is $g^{'}$ , then

$g^{'} = g /9$

$g^{'} = 27 g$

$g^{'} = 9 g$

$g^{'} = 3 g$

$g = \frac{GM}{r ^{2}}$ and $g^{'} = \frac{G M ^{'}}{r ^{2}} [M^{'} = 3 M]$
$\frac{g ^{'}}{g} = \frac{3 M}{M}$
$\Rightarrow g^{'} = 3 g$ .

Q. Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g′, then

g′=g/9

g′=27g

g′=9g

g′=3g