The given statement"If the pressure of a gas sample is quadrupled and the absolute temperature is doubled" is false.
Answer: Option B
<u>Explanation:</u>
As we know the direct relationship between Pressure and Temperature by the Gay-Lussac’s Law,

From this, we get,


So, according to given statement, we have 
Then from the above expression, we can find out the value of
when pressure increased by 4 times of initial pressure as,

Hence, we get,

Hence, from the above expression we can say that as we increase the pressure four times, the temperature does not get doubled. So, the given statement in the question is false.
The answer is C, since the velocity is not changing then neither is the acceleration
Answer:
a)
, b)
, c)
, d) Six polar bears.
Explanation:
a) The slab of ice is modelled by the Archimedes' Principles and the Newton's Laws, whose equation of equilibrium is:

The height of the ice submerged is:




The percentage of the volume of the ice that is submerged is:


b) The height of the portion of the ice that is submerged is:

c) The buoyant force acting on the ice is:


d) The new system is modelled after the Archimedes' Principle and Newton's Laws:

The number of polar bear is cleared in the equation:




The maximum number of polar bears that slab could support is 6.
Answer:
See answer
Explanation:
Given quantities:
![\eta = 0.05\\ W=90[W]\\r=0.0285[m]](https://tex.z-dn.net/?f=%5Ceta%20%3D%200.05%5C%5C%20W%3D90%5BW%5D%5C%5Cr%3D0.0285%5Bm%5D)
where
is the efficiency of the lightbulb (visible light is 5% of the total power),
is the total power of the lightbulb, r is the radius of the lightbulb in meters.
Intensity is power divided by area:

a) Now the effective power is
, therefore:
![I =\frac{\eta*W}{\pi r^2}=\frac{0.05*90}{4\pi (0.0285)^2}=440.87[W/m^2]](https://tex.z-dn.net/?f=I%20%3D%5Cfrac%7B%5Ceta%2AW%7D%7B%5Cpi%20r%5E2%7D%3D%5Cfrac%7B0.05%2A90%7D%7B4%5Cpi%20%280.0285%29%5E2%7D%3D440.87%5BW%2Fm%5E2%5D)
b) Now the intensity is the average poynting vector is related to the magnitudes of the maximum electric field and magnetic field amplitudes, following:
![S_{average}= \frac{EB}{2\mu_{0}}[W/m]](https://tex.z-dn.net/?f=S_%7Baverage%7D%3D%20%5Cfrac%7BEB%7D%7B2%5Cmu_%7B0%7D%7D%5BW%2Fm%5D)
now
and
are related:
and 
replace in 
![S_{average}=I= \frac{c \epsilon_{0}E^2}{2}[W/m]](https://tex.z-dn.net/?f=S_%7Baverage%7D%3DI%3D%20%5Cfrac%7Bc%20%5Cepsilon_%7B0%7DE%5E2%7D%7B2%7D%5BW%2Fm%5D)
we replace the values and we get:

![E = \sqrt{\frac{2(440.8)}{8.85*10^{-12}3*10^8}}=576.24[V/m]](https://tex.z-dn.net/?f=E%20%3D%20%5Csqrt%7B%5Cfrac%7B2%28440.8%29%7D%7B8.85%2A10%5E%7B-12%7D3%2A10%5E8%7D%7D%3D576.24%5BV%2Fm%5D)
therefore
![B=\frac{E}{c}=\frac{576.24}{3*10^{8}}=1.92*10^{-6}[T]](https://tex.z-dn.net/?f=B%3D%5Cfrac%7BE%7D%7Bc%7D%3D%5Cfrac%7B576.24%7D%7B3%2A10%5E%7B8%7D%7D%3D1.92%2A10%5E%7B-6%7D%5BT%5D)