suppose a planet exists whose mass & radies
are half those of earth calculate g on surface of this planet.
Answers
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
"Therefore the acceleration due to gravity on the planet is
Solution:
We know that the "acceleration due to gravity" formula is
g=\frac { GM }{ R^{ 2 } }g=
R
2
GM
Where, M is mass of planet and R is its radius
In earth the "acceleration due to gravity" value g^{\prime}=9.8 \mathrm{m} / \mathrm{s}^{2}g
′
=9.8m/s
2
On planet g' is
{ g }^{ \prime}=\frac { GM }{ { R }^{ 2 } } =\frac { GM }{ 2{ \left( \frac { R }{ 2 } \right)}^{ 2 } } =\frac { 2GM }{ { R }^{ 2 } } =2{ g }g
′
=
R
2
GM
=
2(
2
R
)
2
GM
=
R
2
2GM
=2g