Figure 13-42 shows, not to scale, a cross section through the interior of Earth. Rather than being uniform throughout, Earth is divided into three zones: an outer crust, a mantle, and an inner core. The dimensions of these zones and the masses contained within them are shown on the figure. Earth has a total mass of 5.98 × 10 24 kg and a radius of 6370 km. Ignore rotation and assume that Earth is spherical, (a) Calculate a g at the surface. (b) Suppose that a bore hole (the Mohole) is driven to the crust-mantle interface at a depth of 25.0 km; what would be the value of a g at the bottom of the hole? (c) Suppose that Earth were a uniform sphere with the same total mass and size. What would be the value of a g at a depth of 25.0 km? (Precise measurements of a g are sensitive probes of the interior structure of Earth, although results can be clouded by local variations in mass distribution.) Figure 13-42 Problem 27.
Figure 13-42 shows, not to scale, a cross section through the interior of Earth. Rather than being uniform throughout, Earth is divided into three zones: an outer crust, a mantle, and an inner core. The dimensions of these zones and the masses contained within them are shown on the figure. Earth has a total mass of 5.98 × 10 24 kg and a radius of 6370 km. Ignore rotation and assume that Earth is spherical, (a) Calculate a g at the surface. (b) Suppose that a bore hole (the Mohole) is driven to the crust-mantle interface at a depth of 25.0 km; what would be the value of a g at the bottom of the hole? (c) Suppose that Earth were a uniform sphere with the same total mass and size. What would be the value of a g at a depth of 25.0 km? (Precise measurements of a g are sensitive probes of the interior structure of Earth, although results can be clouded by local variations in mass distribution.) Figure 13-42 Problem 27.
Figure 13-42 shows, not to scale, a cross section through the interior of Earth. Rather than being uniform throughout, Earth is divided into three zones: an outer crust, a mantle, and an inner core. The dimensions of these zones and the masses contained within them are shown on the figure. Earth has a total mass of 5.98 × 1024 kg and a radius of 6370 km. Ignore rotation and assume that Earth is spherical, (a) Calculate ag at the surface. (b) Suppose that a bore hole (the Mohole) is driven to the crust-mantle interface at a depth of 25.0 km; what would be the value of ag at the bottom of the hole? (c) Suppose that Earth were a uniform sphere with the same total mass and size. What would be the value of ag at a depth of 25.0 km? (Precise measurements of ag are sensitive probes of the interior structure of Earth, although results can be clouded by local variations in mass distribution.)
In January 2006 astronomers reported the discovery of a planet, comparable in size to the earth, orbiting another star and having a mass about 5.5 times the earth’s mass. It is believed to consist of a mixture of rock and ice, similar to Neptune. If this planet has the same density as Neptune 11.76 g>cm32, what is its radius expressed (a) in kilometers and (b) as a multiple of earth’s radius?
Assuming the earth to be a sphere of uniform mass density, how much would a body weight half way down to the centre of the earth if it weighed 250 N on the surface?
Assume the Earth is a uniform sphere with constant density. Let R represent the radius of the Earth and g be the acceleration due to gravity at the surface.
At which location above the surface of the earth will the acceleration due to gravity be g/3? Check to see if the answer is correct or/and makes sense.
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