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Your mass density must have units kg/m${}^3$. The simplest way to achieve this is to write the density $$\rho({\bf r}) = \frac{M}{V}\left(\frac{r}{r_0}\right)^2$$ where $r_0$ is a constant having units of distance, and $M$ is the total mass, and $V$ is the volume of the cylinder. We choose $r_0$ by integrating to get the total mass $$ M = \int \rho({\bf r}...


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What you want is $\rho(\textbf{r})=Cr^2$, where $C$ is a constant. Find $C$ by integrating this function over cylinder volume, and equating the result to total mass $m$.


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Everything you did is right. $$\frac{p}{4 \pi r^2 c hf}$$ has dimensions $\frac{1}{[Length]^3}$ You can see this by the following dimensional argument: $p:\frac{[Energy]}{[Time]}$ $\frac{1}{hf}:\frac{1}{[Energy]}$ $\frac{1}{r^2 c}: \frac{[Time]}{[Length]^3}$ Combining all these together, you see that only the $\frac{1}{[Length]^3}$ factor remains. ...


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As the steam gets created from the evaporated liquid at the bottom of the liquid drop, it expands and provides additional pressure acting on the bottom of the liquid drop. The steam does move upwards, but new steam is continually being created so the pressure is able to hold the drop slightly above the surface.


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I think if there is a binary system of stars then the size of neutron stars can be estimated. This method i would call direction estimation because even for most direct observations various theories are always involved. When the neutron star passes over the burning star its intensity is dimmed. How much it is dimmed depends on the size ratio of visible and ...


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I think some cargo holders generally aren't concerned about maintaining pressure, most things survive, it's only when pets and people are involved that pressure becomes an important aspect. If the air pads (I guess you're talking about large bubble wrap) were filled with enough air to be tense on the ground the reduced air pressure at 10,000ft would have a ...


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Ice can be denser than water for certain values of $P,T$. Look at these two pictures taken from here: The darker areas in the second picture denotes areas of greater density. So you can clearly see that when pressure is increased, ice becomes denser than water along the coexistence line. For example at $T=400$ K ice VII is clearly denser than water ...



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