An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 20 N.The radius of the planet is 4.0 × 10⁶ m.What is the mass of Planet X? (G = 6.67 × 10−¹¹ N ⋅ m²/kg²) A) 13 × 10¹⁹ kg B) 17 × 10²² kg C) 9.6 × 10²⁴ kg D) 21 × 10²⁵ kg

Question

Quizplus · Accepted Answer

Using the formula for weight, we have:

W = mg

where W is the weight, m is the mass, and g is the acceleration due to gravity.

On Planet X, we have:

W = 20 N
m = 0.50 kg

We need to find the mass of Planet X, which we can do using the formula for gravitational force:

F = G (m1m2)/r^2

where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of two objects, and r is the distance between them.

On the surface of Planet X, m1 is the mass of the planet, and m2 is the mass of the object (0.50 kg):

F = 20 N
G = 6.67 × 10−11 N⋅m^2/kg^2
m1 = ?
m2 = 0.50 kg
r = 4.0 × 10^16 m

Solving for m1, we get:

m1 = Fr^2/Gm2

m1 = (20 N)(4.0 × 10^16 m)^2/(6.67 × 10−11 N⋅m^2/kg^2)(0.50 kg)

m1 = 9.6 × 10^24 kg

Therefore, the best choice is C, 9.6 × 10^24 kg.

An Object of Mass 0