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 2.30 n on earth. how much would it weigh on jupiter?
□n

Explanation:

Step1: Define proportionality relation

Let $W$ = weight, $M$ = planet mass, $r$ = planet radius. Then $W = k\frac{M}{r^2}$, where $k$ is a constant.

Step2: Set up Earth/Jupiter ratio

For Earth: $W_E = k\frac{M_E}{r_E^2}$. For Jupiter: $W_J = k\frac{M_J}{r_J^2}$. Take the ratio $\frac{W_J}{W_E} = \frac{M_J/M_E}{(r_J/r_E)^2}$.

Step3: Substitute given values

$M_J/M_E = 320$, $r_J/r_E = 11$, $W_E = 2.30\ \text{N}$.
$\frac{W_J}{2.30} = \frac{320}{11^2} = \frac{320}{121}$

Step4: Solve for $W_J$

$W_J = 2.30 \times \frac{320}{121}$

Answer:

$5.99\ \text{N}$ (rounded to three significant figures)