Moment of inertia for one rod is expressed as:
<span>
I(1)= I(end) + md^2 = (1\12)mL^2+m(L/2√2)^2=(5/24)mL^2
</span><span>
Therefore, for two rods:
</span><span>
I2 = 2I1 = (5/12)mL^2
</span><span>
For the moment of inertia at the pivot point,
</span><span>
I=I2+2md^2=(5/12)mL^2+2(m(L/2√2)^2)=(2/3)mL^2
</span><span>
Substituting the equations above to the equation for frequency:
</span><span>
f=(1/2π)√(2mgd/I)=(1/4π)√(6g/√2L)</span>
Area=54
l2=54
l =3√6
volume=(3√6)3
=396.81
The density of the nugget is
and is made of gold
Explanation:
The density of an object can be calculated as

where
d is the density
m is the mass
V is the volume of the object
We have to note that density of an object actually depends on the material the object is made of (therefore, two objects made of the same material can have different mass and different volume, but they have same density).
For the nugget in this problem, we have:
mass: m = 38 g
volume: 
So, its density is

And by looking at the table, we see that this value corresponds approximately to the density of gold, so the nugget is made of gold.
Learn more about density:
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