If the mass of a planet is 10 % less than that of the Earth and the radius 20 % greater than that of the Earth, the acceleration due to gravity on the planet will be

Question

If the mass of a planet is 10 % less than that of the Earth and the radius 20 % greater than that of the Earth, the acceleration due to gravity on the planet will be (A) (5/8) times that on the surface of the Earth (B) (3/4) times that on the surface of the Earth (C) (1/2) times that on the surface of the Earth (D) (9/10) that on the surface of the Earth

Tardigrade Admin · Accepted Answer

g=(G M/R2) g prime=(G((90/100) M)/((120)100 R)2)=((0.9/1.22)) (G M/R2)=(5/8) g

Q. If the mass of a planet is $10%$ less than that of the Earth and the radius $20%$ greater than that of the Earth, the acceleration due to gravity on the planet will be

$\frac{5}{8}$ times that on the surface of the Earth

$\frac{3}{4}$ times that on the surface of the Earth

$\frac{1}{2}$ times that on the surface of the Earth

$\frac{9}{10}$ that on the surface of the Earth

$g = \frac{GM}{R ^{2}}$
$g^{'} = \frac{G ( \frac{90}{100} M )}{( \frac{120}{100} R ) ^{2}} = (\frac{0.9}{1. 2 ^{2}}) \frac{GM}{R ^{2}} = \frac{5}{8} g$

Q. If the mass of a planet is 10% less than that of the Earth and the radius 20% greater than that of the Earth, the acceleration due to gravity on the planet will be

85​ times that on the surface of the Earth

43​ times that on the surface of the Earth

21​ times that on the surface of the Earth

109​ that on the surface of the Earth