Question

The mass of a hypothetical planet is 1/100 that of Earth and its radius is 1/4 that of Earth. If a person weighs 600 N on Earth, what would he weigh on this planet ?

Answer 1

Using Newton's law of gravitation and the given mass and radius data of the hypothetical planet, the weight of a person who weighs 600 N on Earth would be approximately 96 N on that planet.

Step-by-step explanation:

To determine the gravitational force (weight) on a person on a hypothetical planet, we can use Newton's universal law of gravitation. The weight of a person on Earth is given by:

W = m × g

Where m is the mass of the person and g is the acceleration due to gravity on Earth (9.80 m/s²). For a person weighing 600 N on Earth, we have:

m = W/g => m = 600 N / 9.80 m/s² => m ≈ 61.2 kg

To find the weight of this person on the hypothetical planet, we use:

W' = m × g'

Where g' is the gravitational acceleration on the hypothetical planet. Since the planet's mass is 1/100th of Earth's, and its radius is 1/4th of Earth's, by the law of gravitation:

g' = G × (M'/R'²)

But, with M' = M/100 and R' = R/4, we get:

g' = G × (M/100) / (R/4)² => g' = (G × M)/(R²) × 1/100 × 16

As the gravitational acceleration on Earth is g = (G × M)/(R²), then:

g' = g × 1/100 × 16 => g' = g/6.25

Therefore, the weight of the person on the hypothetical planet would be:

W' = m × g/6.25 => W' = 600 N / 6.25 => W' ≈ 96 N

So the person would weigh approximately 96 newtons on the hypothetical planet.

Answer 2

To solve this problem we will apply the Newtonian concept of gravitational acceleration produced by a planet. This relationship is given by:

`g = (GM)/(r^2)`

Where,

G = Gravitational Universal Constant

M = Mass of Earth

r = Radius

The values given are based on the constants of the earth, so they can be expressed as

`M_p = (1)/(100) M_e`

`r_p = (1)/(4) r_e`

The relationship of gravity would then be given:

`g_e = (GM_e)/(r_e^2)`

The relationship with the new planet, from the gravity of the earth would be given

`g_p = (GM_p)/(r_p^2)`

`g_p = (G(1/100)M_e)/((1/4 r_e)^2)`

`g_p = (GM_e 16)/(100 r_e^2)`

`g_p = 0.16 (GM_e)/(r_e^2)`

`g_p = 0.16g_e`

The relationship with the weight of the earth would be given as:

`W_e = m*g_e = 600N`

`W_p = m*g_p = m(0.16g_p)`

`W_p = (m*g_p)(0.16)`

`W_p = 600*0.16`

`W_p = 96N`

Therefore the weigh on this planet would be 96N