Centre of gravity — A/L Combined Mathematics

How do I practise Centre of gravity?

1 question with a worked solution

1. Under what physical condition does the center of gravity (CG) of an extended rigid body coincide exactly with its center of mass (CM)?
   1. A) When the body moves with relativistic speed
   2. B) In a spatially uniform gravitational field
   3. C) Only when the body is in outer space with zero gravity
   4. D) Only when the body is spherical and homogeneous
   Check my answer

   Correct answer: B) In a spatially uniform gravitational field

   The center of mass is the average location of mass distribution (purely geometric/inertial). The center of gravity is the point through which the resultant gravitational force acts. When the gravitational field acceleration g is spatially uniform across the entire body, g factors out of the moment equation, making CG identical to CM.

   Show worked solution

   Step 1: CG = point where resultant gravitational force acts: r_CG = ∑(m_i g_i r_i) / ∑(m_i g_i). Step 2: If g is uniform, g factors out: r_CG = ∑(m_i r_i) / ∑(m_i) = r_CM. Answer: In a spatially uniform gravitational field.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Centre of gravity fit in the syllabus?

Year 2 · Term 2