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

Part a)

`g_(venus) = 8.87 m/s^2`

Part b)

`W = 67.9 N`

Step-by-step explanation:

As we know that the acceleration due to gravity is given as

`g = (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) = (G(0.815M_(earth)))/((0.949R_(earth))^2)`

`g_(venus) = 0.90g_(earth)`

`g_(venus) = 0.90 * 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 * 8.87`

`W = 67.9 N`