Verified Answer :
I'd just keep in mind the relationships for: g = 9.81 m/s²
and universal gravitational acceleration:
ie that:
for MASS, its directly proportional:
a mass that is 0.815 of Earth's would have a gravitational acceleration that's:
0.815g
and
for RADIUS (R) of planet, it's inversely proportional to the square of R
a planet with radius that's 0.949 of Earth's would have a gravitational acceleration of:
(1/0.949)² = 1.11g
the combination of these two effects would be:
(0.815 • 1.11)g = 0.905g = 8.88 m/s²
Answer:
Part a)
\(g_{venus} = 8.87 m/s^2\)
Part b)
\(W = 67.9 N\)
Explanation:
As we know that the acceleration due to gravity is given as
\(g = \frac{GM}{R^2}\)
where we know that
M = mass of planet
R = radius of planet
if we plug in mass of earth and radius of earth in above equation then we will have
\(g = 9.8 m/s^2\)
now if we will find it for Venus
\(M = 0.815M_{earth}\)
\(R = 0.949R_{earth}\)
now from above formula again
\(g_{venus} = \frac{G(0.815M_{earth})}{(0.949R_{earth})^2}\)
\(g_{venus} = 0.90g_{earth}\)
\(g_{venus} = 0.90 \times 9.8\)
\(g_{venus} = 8.87 m/s^2\)
Part b)
If Rock weigh 75 N on surface of Earth
then we have
\(F_g = mg\)
\(75 = m(9.8 m/s^2)\)
\(m = 7.65 kg\)
now on the surface of Venus its weight is given as
\(W = mg_{venus}\)
\(W = 7.65 \times 8.87\)
\(W = 67.9 N\)