MATH103 April 2005
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q2 • Q3 (a) • Q3 (b) • Q3 (c) • Q4 • Q5 (a) • Q5 (b) • Q5 (c) • Q6 (a) • Q6 (b) • Q6 (c) • Q7 (a) • Q7 (b) • Q7 (c) • Q8 (a) • Q8 (b) • Q8 (c) •
Question 01 (e)
Multiple Choice Question: Select ONE correct answer (i), (ii), (iii), (iv), or (v).
(e) Consider the mass density function
over the interval . The centre of mass of this mass distribution is
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
The formula for the centre of mass of a continuous distribution over the interval is
where is the mass density function.
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Given the mass density function over the interval , we use the formula for the centre of mass to get
The integral on the top is calculated as
and the integral on the bottom reduces to
Putting these together we finally obtain
Therefore, the correct answer is (iv).
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