Question

Acceleration due to gravity at surface of a plane
is equal to earth.the density is 1.5 times that of earth. If radius of earth is R, radius of planet ​

Answer 1

Answer:

2R/3

Explanation:

Acceleration due to gravity (g) of a planet of mass "M" and radius "R" is given as:

• g = GM/R²

If "d" is the density of planet and "V" be volume of it then,

• g = GVd/R²

If planet is considered as a perfectly spherical object of volume 4πR³/3 then,

• g = G(4πR³/3)d/R²
• g = 4GdπR/3

From above, for two planets of same acceleration due to gravity, Radius is inversely proportional to Density

Let,

Radius of Earth = R1

Radius of unknown planet = R2

Density of Earth = d1

Density of unknown planet = d2

Then,

R2/R1 = d1/d2

R2 = R1 × d1/d2

R2 = R1 × d1 / (1.5d1)

R2 = R1 × 1/1.5

R2 = R1 × 10/15

R2 = R1 × 2/3

R2 = 2R1/3

It's given that R1 = R

So, R2 = 2R/3