Question

Suppose there exist a planet whose mass is half and radius is double than that
of the Earth. What is the ratio of acceleration due to gravity on this planet to
the acceleration due to gravity on the surface of Earth.

Answer 1

Explanation:

As we know that the acceleration in earth is calculated by the formula

r

2

Gm

which equals 9.8m/s

2

where m is the mass of the earth and r is the radius of the earth.

now,

mass of that planet is half of earth so it's mass is

2

1

(m) and it's radius is half of earth so, it's radius is

2

1

(r)

we will use the same formula to find the gravitational acceleration of that planet which equals

(

2

1

)r

2

G(

2

1

)m

=

4

r

2

2

Gm

=

r

2

2Gm

∗2

now, substitute for

r

2

Gm

of earth

=9.8×2=19.6m/s

2

so, the value of g on that planet will be 19.6m/s

2

Answer 2

Answer:

As we know that the acceleration in earth is calculated by the formula

r

2

Gm

which equals 9.8m/s

2

where m is the mass of the earth and r is the radius of the earth.

now,

mass of that planet is half of earth so it's mass is

2

1

(m) and it's radius is half of earth so, it's radius is

2

1

(r)

we will use the same formula to find the gravitational acceleration of that planet which equals

(

2

1

)r

2

G(

2

1

)m

=

4

r

2

2

Gm

=

r

2

2Gm

∗2

now, substitute for

r

2

Gm

of earth

=9.8×2=19.6m/s

2

so, the value of g on that planet will be 19.6m/s

2