Question

The weight of an object at the surface of a planet is proportional to the planet’s mass and inversely proportional to the square of the radius of the planet. Jupiter’s radius is 11 times Earth’s, and its mass is 320 times Earth’s. An apple weighs 1.40 N on Earth. How much would it weigh on Jupiter?

Answer 1

Given data

*Jupiter's radius is 11 times the Earth's radius is r_j = 11 × r_e

*The mass of Jupiter is 320 times the earth's mass is m_j = 320 × m_e

*An apple weighs on earth is W_e = 1.40 N

As from the given data, the weight of the object is proportional to the mass of the planet and inversely proportional to the square of the radius of the planet. It is given as

`W=(km)/(r^2)`

*Here k is the constant

Now for the earth, the expression for the weight becomes

`W_e=(km_e)/(r^2_e)`

Similarly, for now, the expression becomes for Jupiter as

`W_j=(km_j)/(r^2_j)`

The ratio of the weight of Jupiter to the weight of the earth is given as

`\begin{gathered} (W_j)/(W_e)=(((km_j)/(r^2_j)))/(((km_e)/(r^2_e))) \\ W_j=W_e*(((m_j)/(m_e)))/(((r_j)/(r_e))^2) \end{gathered}`

Substitute the known values in the above expression as

`\begin{gathered} W_j=1.40*(((320m_e)/(m_e)))/(((11r_e)/(r_e))^2) \\ =1.40*(320)/(121) \\ =3.70\text{ N} \end{gathered}`

Hence, the weight of the apple on Jupiter is W_j = 3.70 N