Answer:
As a substance reaches the melting point, the particles begin to move faster, causing the substance to become a liquid.
Explanation:
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Answer:
both statements are truth
Explanation:
a-The Joule effect, also called Joule's law, is the thermal manifestation of electrical resistance. ... In all these cases, it is intended to generate thermal energy with electricity passing through its conductors. This heat they give off is due to the Joule effect.
b-sure of a liquid tank depends only on the density of the liquid and depth from the free surface. It is a scalar quantity and is same in all directions, at a point.
Answer:
First let's write down the moment of inertia of the objects.
![I_{sphere} = \frac{2}{5}mR^2\\I_{disk} = \frac{1}{2}mR^2\\I_{hoop} = mR^2](https://tex.z-dn.net/?f=I_%7Bsphere%7D%20%3D%20%5Cfrac%7B2%7D%7B5%7DmR%5E2%5C%5CI_%7Bdisk%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7DmR%5E2%5C%5CI_%7Bhoop%7D%20%3D%20mR%5E2)
If they all roll without slipping, then the following relation is applied to all ot them:
![v = \omega R](https://tex.z-dn.net/?f=v%20%3D%20%5Comega%20R)
where v is the translational velocity and ω is the rotational velocity.
We will use the conservation of energy, because we know that their initial potential energies are the same. (Here, I will assume that all the objects have the same mass and radius. Otherwise we couldn't determine the difference. )
![K_1 + U_1 = K_2 + U_2\\0 + mgh = \frac{1}{2}I\omega^2 + \frac{1}{2}mv^2](https://tex.z-dn.net/?f=K_1%20%2B%20U_1%20%3D%20K_2%20%2B%20U_2%5C%5C0%20%2B%20mgh%20%3D%20%5Cfrac%7B1%7D%7B2%7DI%5Comega%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7Dmv%5E2)
For sphere:
![\frac{1}{2}\frac{2}{5}mR^2(\frac{v}{R})^2 + \frac{1}{2}mv^2 = mgh\\\frac{1}{5}mv^2 + \frac{1}{2}mv^2 = mgh\\\frac{7}{10}mv^2 = mgh\\v_{sphere} = \sqrt{\frac{10gh}{7}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Cfrac%7B2%7D%7B5%7DmR%5E2%28%5Cfrac%7Bv%7D%7BR%7D%29%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7Dmv%5E2%20%3D%20mgh%5C%5C%5Cfrac%7B1%7D%7B5%7Dmv%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7Dmv%5E2%20%3D%20mgh%5C%5C%5Cfrac%7B7%7D%7B10%7Dmv%5E2%20%3D%20mgh%5C%5Cv_%7Bsphere%7D%20%3D%20%5Csqrt%7B%5Cfrac%7B10gh%7D%7B7%7D%7D)
For disk:
![\frac{1}{2}\frac{1}{2}mR^2(\frac{v}{R})^2 + \frac{1}{2}mv^2 = mgh\\\frac{1}{4}mv^2 + \frac{1}{2}mv^2 = mgh\\\frac{3}{4}mv^2 = mgh\\v_{disk} = \sqrt{\frac{4gh}{3}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Cfrac%7B1%7D%7B2%7DmR%5E2%28%5Cfrac%7Bv%7D%7BR%7D%29%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7Dmv%5E2%20%3D%20mgh%5C%5C%5Cfrac%7B1%7D%7B4%7Dmv%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7Dmv%5E2%20%3D%20mgh%5C%5C%5Cfrac%7B3%7D%7B4%7Dmv%5E2%20%3D%20mgh%5C%5Cv_%7Bdisk%7D%20%3D%20%5Csqrt%7B%5Cfrac%7B4gh%7D%7B3%7D%7D)
For hoop:
![\frac{1}{2}mR^2(\frac{v}{R})^2 + \frac{1}{2}mv^2 = mgh\\\frac{1}{2}mv^2 + \frac{1}{2}mv^2 = mgh\\mv^2 = mgh\\v_{hoop}= \sqrt{gh}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7DmR%5E2%28%5Cfrac%7Bv%7D%7BR%7D%29%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7Dmv%5E2%20%3D%20mgh%5C%5C%5Cfrac%7B1%7D%7B2%7Dmv%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7Dmv%5E2%20%3D%20mgh%5C%5Cmv%5E2%20%3D%20mgh%5C%5Cv_%7Bhoop%7D%3D%20%5Csqrt%7Bgh%7D)
The sphere has the highest velocity, so it arrives the bottom first. Then the disk, and the hoop arrives the last.
Explanation:
The moment of inertia can be defined as the resistance to the rotation. If an object has a high moment of inertia, it resist to rotate more so its angular velocity would be lower. In the case of rolling without slipping, the angular velocity and the linear (translational) velocity are related by the radius, so the object with the highest moment of inertia would arrive the bottom the last.
The correct answer is C. Its speed
Speed is related to the kinetic energy, not the potential one because kinetic requires the body to be in motion, that is, move at a certain speed. Potential energy has no motion.
In order to operate the theremin, a conducting object must be moved within the electric fields produced by the instrument