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larisa [96]
3 years ago
7

Two spherical shells have their mass uniformly distrubuted over the spherical surface. One of the shells has a diameter of 2 met

ers and a mass of 1 kilogram. The other shell has a diameter of 1 meter. What must the mass m of the 1-meter shell be for both shells to have the same moment of inertia about their centers of mass?
Mathematics
1 answer:
ivann1987 [24]3 years ago
7 0
The moment of inertia of a spherical shell is I = mr²

If two spheres have the same moment of inertia, then
I₁ = I₂
m₁(r₁)² = m₂(r₂)²

Solve for the second mass:
m₂ = m₁ (r₁/r₂)²

Given m₁ = 1 kg, r₁ = 2 m, r₂ = 1m,
m₂ = (1 kg) (2 m / 1 m)² = 4 kg

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Afina-wow [57]

Answer:

d)\ \frac{81}{m^{7}}

Step-by-step explanation:

(3m^-4)^3(3m^5)

First, simplify (3m^{-4})^3:

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3 years ago
Read 2 more answers
Please answer this correctly without making mistakes
tankabanditka [31]

Answer:

263.76

Step-by-step explanation:

Assuming the shaded area is the yellow area all we must do is find the area of the small circle and subtract it from the larger circle.

To do this we can use the area of a circle equation:

A=\pi r^2

first we need to find the radius of the large circle which is simply 4+6= 10

so the area would be:

A=\pi 10^2\\A=100\pi

then we find the area of the small circle is

A=4^2\pi \\A=16 pi

next we evaluate:

100\pi -16\pi =84\pi

Then replace pi with 3.14:

84 · 3.14 = 263.76

And you have your answer!

Hope this helps!

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3 years ago
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