Calculating Density and R of a Compound Pendulum

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To calculate the density p(x,y) of an equilateral triangle suspended as a compound pendulum, the area A is determined as A = (sqrt(3)/4) * B^2, leading to p(x,y) = (4*sqrt(3)*m)/(3*B^2). The distance R from the pivot point to the center of gravity is calculated using R = (B/2)*(2/sqrt(3)), resulting in R = (sqrt(3)*B)/3. The calculations provided appear to be correct based on the formulas used. The discussion confirms the accuracy of the solution presented.
Akibarika
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Little help in compound pendulum

Homework Statement


there is an equilateral triangle T with sides of length B. Suspend this triangle from a pivot through on of its corners, so that it is free to swing about this corner in the plane of the tringle.

I want to ask how to compute the density p(x,y) and the R whcih from the pivot point to the center of gravity of the triangle.

In fact I found the soluation, but I don't know it is right or not.
Could anyone check it with me?

Homework Equations


p(x,y)=m/A


The Attempt at a Solution


A=sqrt(3)/4 * B^2
therefore p(x,y)=(4*sqrt(3)*m)/(3*B^2)

about the R:
GRAPH.jpg

cos 30 = sqrt(3)/2
R = (B/2)*(2/sqrt(3)) = (sqrt(3)*B)/3

did I make any mistake??

Thanks a lot
 
Last edited:
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