Answer:
Check the first and the third choices:
<u><em /></u>
- <u><em>a. The temperature of a gas is directly proportional to its volume</em></u>
- <u><em>b. The temperature-to-volume ratio of a gas is constant.</em></u>
Explanation:
Rewrite the table for better understanding:
Temperature of gas (K) Volume of gas (L)
298 4.55
315 4.81
325 4.96
335 ?
Calculate the ratios temperature to volume with 3 significant figures:
Then, those numbers show a <u><em>constant temperature-to-volume ratio</em></u>, which may be expressed in a formula as:
- Temperature / Volume = constant, which is a directly proportional variation (the volume increases in a constant proportion to the increase of the temperature).
Hence, the correct choices are:
- The temperature of a gas is directly proportional to its volume (first statement), and
- The emperature-to-volume ratio of a gas is constant (third statement).
Answer:
The answer is below
Explanation:
a) The initial velocity (u) = 24 m/s
We can solve this problem using the formula:
v² = u² - 2gh
where v = final velocity, g= acceleration due to gravity = 9.8 m/s², h = height.
At maximum height, the final velocity = 0 m/s
v² = u² - 2gh
0² = 24² - 2(9.8)h
2(9.8)h = 24²
2(9.8)h = 576
19.6h = 576
h = 29.4 m
b) The time taken to reach the maximum height is given as:
v = u - gt
0 = 24 - 9.8t
9.8t = 24
t = 2.45 s
The total time needed for the apple to return to its original position = 2t = 2 * 2.45 = 4.9 s
Answer:
Explanation:
Flux through the coil = nBA , n is no of turns , B is magnetic flux and A a is area of the coli
= 200 x 5.6 x 10⁻⁵ x 11.8 x 10⁻⁴
= 13216 x 10⁻⁹ weber .
b ) When the coil becomes parallel to magnetic field , flux through it will become zero.
c ) e m f induced = change in flux / time
= 13216 x 10⁻⁹ / 4.9 x 10⁻²
= 2697.14 x 10⁻⁷ V
= 269.7 x10⁻⁶
269.7 μV.
There's only one question there.
The answer is "Greater amplitude".
Answer:
0.0031792338 rad/s
Explanation:
= Angle of elevation
y = Height of balloon
Using trigonometry
![tan\theta=y\dfrac{y}{200}\\\Rightarrow y=200tan\theta](https://tex.z-dn.net/?f=tan%5Ctheta%3Dy%5Cdfrac%7By%7D%7B200%7D%5C%5C%5CRightarrow%20y%3D200tan%5Ctheta)
Differentiating with respect to t we get
![\dfrac{dy}{dt}=\dfrac{d}{dt}200tan\theta\\\Rightarrow \dfrac{dy}{dt}=200sec^2\theta\dfrac{d\theta}{dt}\\\Rightarrow 100=200sec^2\theta\dfrac{d\theta}{dt}\\\Rightarrow \dfrac{d\theta}{dt}=\dfrac{100}{200sec^2\theta}\\\Rightarrow \dfrac{d\theta}{dt}=\dfrac{1}{2}cos^2\theta](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdt%7D%3D%5Cdfrac%7Bd%7D%7Bdt%7D200tan%5Ctheta%5C%5C%5CRightarrow%20%5Cdfrac%7Bdy%7D%7Bdt%7D%3D200sec%5E2%5Ctheta%5Cdfrac%7Bd%5Ctheta%7D%7Bdt%7D%5C%5C%5CRightarrow%20100%3D200sec%5E2%5Ctheta%5Cdfrac%7Bd%5Ctheta%7D%7Bdt%7D%5C%5C%5CRightarrow%20%5Cdfrac%7Bd%5Ctheta%7D%7Bdt%7D%3D%5Cdfrac%7B100%7D%7B200sec%5E2%5Ctheta%7D%5C%5C%5CRightarrow%20%5Cdfrac%7Bd%5Ctheta%7D%7Bdt%7D%3D%5Cdfrac%7B1%7D%7B2%7Dcos%5E2%5Ctheta)
Now, with the base at 200 ft and height at 2500 ft
The hypotenuse is
![h=\sqrt{200^2+2500^2}\\\Rightarrow h=2507.98\ ft](https://tex.z-dn.net/?f=h%3D%5Csqrt%7B200%5E2%2B2500%5E2%7D%5C%5C%5CRightarrow%20h%3D2507.98%5C%20ft)
Now y = 2500 ft
![cos\theta=\dfrac{200}{h}\\\Rightarrow cos\theta=\dfrac{200}{2507.98}=0.07974](https://tex.z-dn.net/?f=cos%5Ctheta%3D%5Cdfrac%7B200%7D%7Bh%7D%5C%5C%5CRightarrow%20cos%5Ctheta%3D%5Cdfrac%7B200%7D%7B2507.98%7D%3D0.07974)
![\dfrac{d\theta}{dt}=\dfrac{1}{2}\times 0.07974^2\\\Rightarrow \dfrac{d\theta}{dt}=0.0031792338\ rad/s](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%5Ctheta%7D%7Bdt%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%200.07974%5E2%5C%5C%5CRightarrow%20%5Cdfrac%7Bd%5Ctheta%7D%7Bdt%7D%3D0.0031792338%5C%20rad%2Fs)
The angle is changing at 0.0031792338 rad/s