Question

THE MASS OF VENUS IS 81.5% OF THE EARTH AND ITS RADIUS IS 94.9% THAT OF THE EARTH. A)COMPUTE THE ACCELERATION DUE TO GRAVITY ON THE SURFACE OF VENUS FROM THESE DATA.B)IF A ROCK WEIGHS 75.0N ON EARTH,WHAT WOULD IT WEIGH ON THE SURFACE OF VENUS?

Answer 1

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 2

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

$W = mg_{venus}$

$W = 7.65 \times 8.87$

$W = 67.9 N$