The density inside a solid sphere of radius a is given by p=Po a/r, where Po is the density at the surface and r denotes the distance from the center. Find the gravitational field due to this sphere at a distance 2 a from its center.
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- Sphere A with mass 70 kg is located at the origin of an xy coordinate system; sphere B with mass 73 kg is located at coordinates ( 0.23 m, 0); sphere C with mass 0.55 kg is located at coordinates ( 0.15 m, 0.14 m). In unit-vector notation, what is the gravitational force on C due to A and B?In the figure, three 8.28 kg spheres are located at distances d1 = 0.415 m, and d2 = 0.414 m. What are the (a) magnitude and (b) direction (relative to the positive direction of the x axis) of the net gravitational force on sphere B due to spheres A and C? di В (a) Number i Units (b) Number UnitsFive small spheres each with a mass of 48 kg are attached to the vertices of a pentagon. A set of coordinate axes are chosen such that the pentagon lies in the x,y plane with the origin at the center of the pentagon, and one of the spheres is located along the x axis 8 meters from the origin. See figure below. Find the z component of the gravitational field due to these five point masses at a point P on the z axis a distance 6 meters from the origin. Use G = 6.673E-11 N m2/kg2.
- Chapter 13, Problem 011 In the figure, two spheres of mass m = 9.24 kg. and a third sphere of mass M form an equilateral triangle, and a fourth sphere of mass mą is at the center of the triangle. The net gravitational force on that central sphere from the three other spheres is zero. (a) What is the value of mass M? (b) If we double the value of m4, what then is the magnitude of the net gravitational force on the central sphere? M (a) Number Units (b) Number Units Click if you would like to Show Work for this question: Open Show Work Question Attempts: 0 of 10 used SUBMIT ANSWER SAVE FOR LATERNewton's theory of gravity, together with the Cavendish experiment to measure the value of Newton's constant G, determines the acceleration due to gravity at the surface of a sphere. For example, the acceleration due to gravity at the surface of Earth is g 9.81 m/s^2. Calculate the acceleration due to gravity at the surface of the sun, which has mass 1.989x10 30 kg and 6.96x108 m. radius = (in m/s^2) A: 112.2 OB: 140.2 OC: 175.3 OD: 219.1 OE: 273.9 OF: 342.3 OG: 427.9 OH: 534.9In the figure, three 9.74 kg spheres are located at distances d₁ = 0.953 m, and d₂ = 0.215 m. What are the (a) magnitude and (b) direction (relative to the positive direction of the x axis) of the net gravitational force on sphere B due to spheres A and C? (a) Number i (b) Number i dr B Units Units î ✪
- Planet Kling has half the radius and 2 times the mass of the Earth. What is the best estimate for the magnitude of the gravitational field at the surface of Planet Kling?Tidal forces are gravitational forces exerted on different parts of a object by a second object. Their effects are particularly visible on Earth's surface in the form of tides. To understand the origin of tidal forces, consider Earth-Moon system to consist of two spherical bodies, each with a spherical mass distribution. Let RE be the radius of Earth, m be the mass of the Moon, and G be the gravitational constant. Part B Since the gravitational force between two bodies decreses with distance, the accelaeration a(near) experienced by a unit mass located at the point on the earth's surface closest to moon is slightly different from the acceleration a(far) experienced by a unit mass located at the point on the earth`s surface farthest from the moon. Give a general expresion for the quantity a(near)- a(far).A 4.4 kg mass weighs 35.64 N on the surfaceof a planet similar to Earth. The radius ofthis planet is roughly 6 × 10^6 m.Calculate the mass of of this planet. Thevalue of the universal gravitational constantis 6.67259 × 10^−11 N · m^2/kg^2.Answer in units of kg. Calculate the average density of this planet.Answer in units of kg/m^3.
- A sphere of copper has a radius of 50.0 cm and a mass of 4690 kg. A sphere of unknown metal has a radius of 30.0 cm. The surfaces of the spheres are 20.0 cm apart. The force of gravitational attraction between the two spheres is 0.372 mN. What is the mass of the unknown metal?Consider a spherical shell constructed from a material of density 6.1 x 103 kg/m3. The inner radius of the shell is 4.9 x 106 m from the center, and the outer radius of the shell is 9.2 x 106 m from the center. Calculate the magnitude of the gravitational field 13.1 x 106 m from the center of the shell, in N/kg. Use G = 6.7 x 10-11 N m2 / kg2. (Please answer to the fourth decimal place - i.e 14.3225)A sphere of copper has a radius of 50.0 cm and a mass of 4690 kg. A sphere of unknown metal has a radius of 30.0 cm. The surfaces of the sphere are 20.0 cm apart. The force of gravitational attraction between the two spheres is 0.372 nM. What is the mass of the unknown metal?