Answer:
Sound energy is produced when an object vibrates. The sound vibrations cause waves of pressure that travel through a medium, such as air, water, wood or metal. Sound energy is a form of mechanical energy.
Explanation:
<span>The velocity would be 54.2 m/s
We would use the equation 1/2mv^2top+mghtop = 1/2mv^2bottom+mghbottom where m is the mass of the bobsled(which can be ignored), vtop/bottom is the velocity of the bobsled at the top or bottom, g is gravity, and htop/bottom is the height of the bobsled at the top or bottom of the hill. Since the velocity of the bobsled at the top of the hill and height at the bottom of the hill are zero, 1/2mv^2top and mghbottom will equal zero. The equation will be mghtop=1/2mv^2bottom. Thus we would solve for v.</span>
This leads to a paradox known as the Gibbs paradox, after Josiah Willard Gibbs. The paradox allows for the entropy of closed systems to decrease, violating the second law of thermodynamics. A related paradox is the "mixing paradox".
Answer:
M
Explanation:
To apply the concept of <u>angular momentum conservation</u>, there should be no external torque before and after
As the <u>asteroid is travelling directly towards the center of the Earth</u>, after impact ,it <u>does not impose any torque on earth's rotation,</u> So angular momentum of earth is conserved
⇒![I_{1} \times W_{1} =I_{2} \times W_{2}](https://tex.z-dn.net/?f=I_%7B1%7D%20%5Ctimes%20W_%7B1%7D%20%3DI_%7B2%7D%20%5Ctimes%20W_%7B2%7D)
-
is the moment of interia of earth before impact -
is the angular velocity of earth about an axis passing through the center of earth before impact
is moment of interia of earth and asteroid system
is the angular velocity of earth and asteroid system about the same axis
let ![W_{1}=W](https://tex.z-dn.net/?f=W_%7B1%7D%3DW)
since ![\text{Time period of rotation}∝](https://tex.z-dn.net/?f=%5Ctext%7BTime%20period%20of%20rotation%7D%E2%88%9D)
![\frac{1}{\text{Angular velocity}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Ctext%7BAngular%20velocity%7D%7D)
⇒ if time period is to increase by 25%, which is
times, the angular velocity decreases 25% which is
times
therefore
![\frac{4}{5} \times W_{1}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B5%7D%20%5Ctimes%20W_%7B1%7D)
(moment of inertia of solid sphere)
where M is mass of earth
R is radius of earth
![I_{2}=\frac{2}{5} \times M\times R^{2}+M_{1}\times R^{2}](https://tex.z-dn.net/?f=I_%7B2%7D%3D%5Cfrac%7B2%7D%7B5%7D%20%5Ctimes%20M%5Ctimes%20R%5E%7B2%7D%2BM_%7B1%7D%5Ctimes%20R%5E%7B2%7D)
(As given asteroid is very small compared to earth, we assume it be a particle compared to earth, therefore by parallel axis theorem we find its moment of inertia with respect to axis)
where
is mass of asteroid
⇒ ![\frac{2}{5} \times M\times R^{2} \times W_{1}=}(\frac{2}{5} \times M\times R^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B5%7D%20%5Ctimes%20M%5Ctimes%20R%5E%7B2%7D%20%5Ctimes%20W_%7B1%7D%3D%7D%28%5Cfrac%7B2%7D%7B5%7D%20%5Ctimes%20M%5Ctimes%20R%5E%7B2%7D)
![M_{1}\times R^{2})\times(\frac{4}{5} \times W_{1})](https://tex.z-dn.net/?f=M_%7B1%7D%5Ctimes%20R%5E%7B2%7D%29%5Ctimes%28%5Cfrac%7B4%7D%7B5%7D%20%5Ctimes%20W_%7B1%7D%29)
=
+ ![M_{1}\times R^{2})](https://tex.z-dn.net/?f=M_%7B1%7D%5Ctimes%20R%5E%7B2%7D%29)
![\frac{1}{10} \times M\times R^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B10%7D%20%5Ctimes%20M%5Ctimes%20R%5E%7B2%7D)
⇒![M_{1}=}](https://tex.z-dn.net/?f=M_%7B1%7D%3D%7D)
![\frac{1}{10} \times M](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B10%7D%20%5Ctimes%20M)