From the case we know that:
- The moment of inertia Icm of the uniform flat disk witout the point mass is Icm = MR².
- The moment of inerta with respect to point P on the disk without the point mass is Ip = 3MR².
- The total moment of inertia (of the disk with the point mass with respect to point P) is I total = 5MR².
Please refer to the image below.
We know from the case, that:
m = 2M
r = R
m2 = 1/2M
distance between the center of mass to point P = p = R
Distance of the point mass to point P = d = 2R
We know that the moment of inertia for an uniform flat disk is 1/2mr². Then the moment of inertia for the uniform flat disk is:
Icm = 1/2mr²
Icm = 1/2(2M)(R²)
Icm = MR² ... (i)
Next, we will find the moment of inertia of the disk with respect to point P. We know that point P is positioned at the arc of the disk. Hence:
Ip = Icm + mp²
Ip = MR² + (2M)R²
Ip = 3MR² ... (ii)
Then, the total moment of inertia of the disk with the point mass is:
I total = Ip + I mass
I total = 3MR² + (1/2M)(2R)²
I total = 3MR² + 2MR²
I total = 5MR² ... (iii)
Learn more about Uniform Flat Disk here: brainly.com/question/14595971
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Answer:
The second projectile was 1.41 times faster than the first.
Explanation:
In the ballistic pendulum experiment, the speed (v) of the projectile is given by:
<em>where m: is the mass of the projectile, M: is the mass of the pendulum, g: is the gravitational constant and h: is the maximum height of the pendulum. </em>
To know how many times faster was the second projectile than the first, we need to take the ratio for the velocities for the projectiles 2 and 1:
(1)
<em>where m₁ and m₂ are the masses of the projectiles 1 and 2, respectively, and h₁ and h₂ are the maximum height reached by the pendulum by the projectiles 1 and 2, respectively. </em>
Since the projectile 1 has the same mass that the projectile 2, we can simplify equation (1):
Therefore, the second projectile was 1.41 times faster than the first.
I hope it helps you!
Your answer is 311.29271 lbs
Answer:
Satellite D has a mass (kg) of 500 and the distance from Earth (km) is 320.
Explanation:
The universal law of gravitation states that the force between two objects in the universe is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
We have to choose the satellite having greatest gravitational force with earth. In all options the distance from the earth is same i.e. 320 km. So, we have to select the satellite having maximum mass because the mass of the earth is constant.
Hence, the correct option is (D) " Satellite D has a mass (kg) of 500 and the distance from Earth (km) is 320 ".
The correct answer is (a.) Hydra. Hydra is not a dwarf planet, instead, it is the moon of the dwarf planet, Pluto. There are only four accepted dwarf planets by the International Astronomical Union which were the Haumea, Pluto, Eris, and Makemake.
