An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 10 N. The radius of the planet is 4.0 × 106 m. What free fall acceleration will the 0.50 kg object experience when transported to a distance of 2.0 × 106 m from the surface of this planet?Select one:a.18 m/s2b.13 m/s2c.90 m/s2d.8.9 m/s2
Question
An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 10 N. The radius of the planet is 4.0 × 106 m. What free fall acceleration will the 0.50 kg object experience when transported to a distance of 2.0 × 106 m from the surface of this planet?Select one:a.18 m/s2b.13 m/s2c.90 m/s2d.8.9 m/s2
Solution
First, we need to find the gravitational constant (G) of Planet X. We can use the formula for the force of gravity:
F = G * (m1 * m2) / r^2
Where: F is the force of gravity (which is the weight of the object on the planet, 10 N), m1 is the mass of the object (0.50 kg), m2 is the mass of Planet X (which we're trying to find), r is the distance between the centers of the two objects (which is the radius of the planet, 4.0 × 10^6 m).
Rearranging the formula to solve for G gives us:
G = F * r^2 / (m1 * m2)
Substituting the known values gives us:
G = 10 N * (4.0 × 10^6 m)^2 / (0.50 kg * m2)
Solving for m2 gives us:
m2 = 10 N * (4.0 × 10^6 m)^2 / (0.50 kg * G)
Next, we can find the free fall acceleration (g) at a distance of 2.0 × 10^6 m from the surface of the planet. The formula for g is:
g = G * m2 / r^2
Where r is now the radius of the planet plus the 2.0 × 10^6 m distance from the surface. Substituting the known values gives us:
g = G * m2 / (4.0 × 10^6 m + 2.0 × 10^6 m)^2
Solving this equation will give us the free fall acceleration at the specified distance from the planet.
Similar Questions
An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 10 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)Select one:a.4.8 × 1024 kgb.17 × 1022 kgc.9.6 × 1024 kgd.13 × 1019 kg
An object is allowed to fall freely near the surface of a planet. The object has an acceleration due to gravity of 24 m/s2. How far does the object fall after the first second?A 4.9 metersB 9.8 metersC 12 metersD 24 meters
The acceleration due to gravity at the surface of Planet X is 10 m/s2. What is the acceleration due to gravity at an altitude of 4000 km above the surface of this planet?Select one:a.More information is needed.b.8.0 m/s2c.4.4 m/s2d.10 m/s2
The acceleration of free fall on the surface of planet P is one-tenth of that on the surface ofplanet Q.On the surface of P, an object has a mass of 1.0 kg and a weight of 1.0 N.What are the mass and the weight of the same object on the surface of planet Q?mass on Q / kg weight on Q / NA 1.0 0.1B 1.0 10C 10 10D 10 100
If a planet has a radius 20% greater than that of the Earth but has the same mass as the Earth, what is the acceleration due to gravity at its surface?Select one:a.8.2 m/s2b.6.8 m/s2c.12 m/s2d.14 m/s2
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.