Question

What would be the acceleration due to gravity on a planet whose mass is 1/12th the mass of earth and radius half the radius of earth. Take g=9.8ms^-2​

Answer 1

Answer:

the acceleration due to gravity g(planet) = 3.26

Explanation:

Radius of earth

$Re = 6400km$

Mass of the earth

$Me = 6 \times 10 ^{24} kg$

According to the question,

Radius of planet

$Rp = \frac{ Re}{2}$

Mass of planet

$Mp = \frac{ Me}{12}$

Now the formula of acceleration due to gravity is,

$g(earth) = \frac{GMe}{ {Re}^{2} } \\ g(planet) = \frac{GMp}{ {Rp}^{2} } \: \\ = \frac{GMe}{12} \times \frac{4}{ {Re}^{2} } \\ = \frac{GMe}{3{Re}^{2}}$

Now, substituting g(earth) in g(planet)

$g(planet) = \frac{g(earth) }{3} \\ = \frac{9.8}{3} \\ = 3.26$