What is the solution to the tricky pendulum question on page 6?

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The discussion revolves around solving a pendulum question from a physics admissions test. The user struggles with calculating the center of mass (COM) for a uniform rod and a pendulum with a bob, substituting appropriate values for distance. They also attempt to determine the time period difference needed for a pendulum to account for a one-day discrepancy, calculating values for brass and invar. Additionally, they express confusion about a geometric question involving an equilateral triangle inscribed in a circle, seeking guidance. Overall, the thread highlights challenges in applying physics concepts to specific problems.
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Homework Statement

hey sorry about this again but I'm having trouble with some questions :o:

http://www.physics.ox.ac.uk/Admissions/undergraduate/admissions_test/tests07.pdf

The Attempt at a Solution



page 6) okay well the bit I'm not sure about here is that L(cm) seeing as it is the distance to the COM i substituted r/2 for the uniform rod and r for the one with the bob giving me;

forma.jpg


i guess it makes sense because it would go to my simplified versions when simplified

then with the 24 hour one it's really tricky...

i worked out how much a time period would be to give a difference of 1 day + 1 second, then I worked out what the difference in r would be which gave me;

0.469K for brass and
7.429K for invar, do you think that's reasonable?

note i used the formula for a pendulum of negligible mass and a mass on the end.and

page 10) question 6, I literally have no idea, i KNOW that it's a silly rule or something reguarding a equilateral triangle in a circle or some rule you can draw on however I'm just blank on this one, any pointers in the right direction would be great...

thanks again!
 
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bump, i know it's a lot to ask but some help would be great
 

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