Olivia wants to find out whether a substance will fluoresce. She says she should put it in a microwave oven. Do you agree with h
2 answers:
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Answer:
The correct answer is D /
= 1.5
Explanation:
In this exercise the moment of inertia equation should be used
I = ∫ r² dm
In addition to the parallel axis theorem
I = + M D²
Where is the moment of the center of mass, M is the total mass of the body and D the distance from this point to the axis of interest
Let's apply these relationships to our problem, the center of mass of a uniform rod coincides with its geometric center, in this case the rod is 1 m long, so the center of mass is in
L = 100.00 cm (1m / 100 cm) = 1.0000 m
= 50 cm = 0.50 m
Let's calculate the moment of inertia for this point, suppose the rod is on the x-axis and use the concept of linear density
λ = M / L = dm / dx
dm = λ dx
Let's replace in the moment of inertia equation
I = ∫ x² ( λ dx)
We integrate
I = λ x³ / 3
We evaluate between the lower limits x = -L/2 to the upper limit x = L/2
I = λ/3 [(L/2)³ - (-L/2)³] = lam/3 [L³/8 - (-L³ / 8)]
I = λ/3 L³/4
I = 1/12 λ L³
Let's replace the linear density with its value
I = 1/12 (M/L) L³
I = 1/12 M L²
Let's calculate with the given values
I = 1/12 M 1²
I = 1/12 M
This point is the center of mass of the rod
Icm = I = 1/12 M = 8.333 10-2 M
Now let's use the parallel axis theorem to calculate the moment of resection of the new axis, which is 0.30 m from one end, in this case the distance is
D = - x
D = 0.50 - 0.30
D = 0.20 m
Let's calculate
=
+ M D²
= 1/12 M + M 0.202
= M (1/12 + 0.04)
= M 0.123
To find the relationship between the two moments of inertia, divide the quantities
/
= M 0.123 / (M 8.3 10-2)
/
= 1.48
The correct answer is d 1.5
Answer:
<em>B) 1.0 × 10^5 V</em>
Explanation:
<u>Electric Potential Due To Point Charges </u>
The electric potential produced from a point charge Q at a distance r from the charge is
The total electric potential for a system of point charges is equal to the sum of their individual potentials. This is a scalar sum, so direction is not relevant.
We must compute the total electric potential in the center of the square. We need to know the distance from all the corners to the center. The diagonal of the square is
where a is the length of the side.
The distance from any corner to the center is half the diagonal, thus
The total potential is
Where V1 and V2 are produced by the +4\mu C charges and V3 and V4 are produced by the two opposite charges of . Since all the distances are equal, and the charges producing V3 and V4 are opposite, V3 and V4 cancel each other. We only need to compute V1 or V2, since they are equal, but they won't cancel.
The total potential is