Science:Math Exam Resources/Courses/MATH103/April 2016/Question 04 (b)
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Question 04 (b) 

The density of a metal bar 3 metres long is is given by kilograms per metre (). Find the centre of mass of the bar. 
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! 
Hint 

Let be the mass of the bar (obtained in Question 04 (a)) and its moment. Then the centre of mass of the bar, , is given by 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. To find the centre of mass of the bar, we first need to compute its mass and the moment. From Question 04 (a), we know that the mass of the bar is On the other hand, the moment of the bar is By the change of variable we have Therefore, by the formula for the centre of mass in the hint, we have 