Because their is nothing at the geographical poles that attracts the magnet
Answer:
P = 0.27R from the center
Explanation:
Given,
The radius of the uniform circular plate, R = 2R
The radius of the hole, r = R
The center of the smaller circle from the center is, d = 0.8R
The center of mass of a circular disc with a hole in it given by the formula
P = dr²/R² - r²
Where P is the distance from the center of mass located in the line joining the two centers opposite to the hole.
Substituting the given values in the above equation,
P = 0.8R x R² / 4R² - R²
= 0.27R³/R²
= 0.27R
Hence the center of mass of plate is at a distant P = 0.27R from the center
Answer: The magnitude of the force exerted on the roof is 490522.5 N.
Explanation:
The given data is as follows.
Below the roof,
= 0 m/s
At top of the roof,
= 39 m/s
We assume that
is the pressure at lower surface of the roof and
be the pressure at upper surface of the roof.
Now, according to Bernoulli's theorem,


= ![0.5 \times 1.29 \times [(39)^{2} - (0)^{2}]](https://tex.z-dn.net/?f=0.5%20%5Ctimes%201.29%20%5Ctimes%20%5B%2839%29%5E%7B2%7D%20-%20%280%29%5E%7B2%7D%5D)
= 
= 981.045 Pa
Formula for net upward force of air exerted on the roof is as follows.
F = 
= 
= 490522.5 N
Therefore, we can conclude that the magnitude of the force exerted on the roof is 490522.5 N.
The period of a simple pendulum is given by:

where L is the length of the pendulum and g is the gravitational acceleration.
The pendulum in our problem makes one complete vibration in 0.333 s, so its period is T=0.333 s. Using this information, we can re-arrange the previous formula to find the length of the pendulum, L: