What is the gravitational field strength at a distance 'R' from the center of a planet of radius 'R' and uniform density?

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Q: What is the gravitational field strength at a distance 'R' from the center of a planet of radius 'R' and uniform density?

Solution: Inside a uniform sphere, the gravitational field strength varies linearly with distance from the center, so at R/2 it is g/2.

Steps: 7

Step 1: Understand that we are looking for the gravitational field strength at a distance 'R' from the center of a planet.
Step 2: Recognize that 'R' is also the radius of the planet.
Step 3: Know that inside a uniform sphere, the gravitational field strength decreases as you move away from the center.
Step 4: Remember that at the center of the planet, the gravitational field strength is 0.
Step 5: Realize that as you move outward from the center to the surface, the gravitational field strength increases linearly.
Step 6: At the surface of the planet (distance 'R' from the center), the gravitational field strength is at its maximum value, which we can call 'g'.
Step 7: Since we are at the surface (distance 'R'), the gravitational field strength is 'g'.