There are 2 spheres of same material and radius. One is hollow and other is solid. If they are heated to the same temperature which expands more the solid, the hollow or they both expand the same?
Intelligent question! Hollow object contains air within, which is poor conductor of heat and can be compressed to a lesser volume. On the other hand, the other one is solid(assuming they are good conductor of heat). If uniform heat is applied to both of them at same rate, the solid one should expand slowly, as it contains more mass plus heat transfer rate between the particles are faster and to expand all the particles need to attain same K Energy at same temperature. While the hollow one contains air which prevents uniform heat distribution within the sphere or rather slow distribution occurs. As it has less matters, so less molecular bond energy need to break and so the expansion is rapid. Instead of expansion, you might see explosion upon strong heating.
A hole is made at the bottom of the tank filled with water. if the total pressure at the bottom is 3 atmospheres, then what is the velocity of efflux?
you can apply Bernoulli’s equation to get the velocity. the dynamic pressure is 2 atmosphere. sov=sqrt(2*2*101325/1000)=20.13 m/sec
What is longitudinal, circumferential and radial stress in a pipe in a practical way? How is radial stress compressive in nature?
When a thin – walled cylinder is subjected to internal pressure, three mutually perpendicular principal stresses will be set up in the cylinder materials, namely• Circumferential or Hoop stress• Radial stress• Longitudinal stressInternal pressure can be produce by water, gases or others. Now let us define these stresses and determine the expressions for them.Circumferential or Hoop stress: This is the stress which is set up in resisting the bursting effect of the applied internal pressure and can be most conveniently treated by considering the equilibrium of the cylinder. The hoop stress is the force exerted circumferentially (perpendicular both to the axis and to the radius of the object) in both directions on every particle in the cylinder wall.In the figure we have shown a one half of the cylinder. This cylinder is subjected to an internal pressure p.i.e. p = internal pressured = inside diametreL = Length of the cylindert = thickness of the wallTotal force on one half of the cylinder owing to the internal pressure 'p'= p x Projected Area= p x d x L= p .d. L ------- (1)The total resisting force owing to hoop stresses(Hs) set up in the cylinder walls= 2 . Hs.L.t ---------(2)Because (Hs.L.t) is the force in the one wall of the half cylinder.from e
If water is kept in vessels of different volumes, at the same level, the base area of each vessel being equal, then will the force experienced by the base of all the vessels be same? If so, why?
The forces experienced by the two bases are indeed the same. From a physical perspective, we can consider the standard gravitationally-induced pressure equation:[math]P = \rho g h[/math]Assuming the two vessels are filled with the same fluid (i.e. the fluids' densities are equal), the pressures are the same for both vessels, because the heights are the equal. Since both bases have the same area, and P = F/A, the forces on the bases are therefore equal.Why is this the case?Well, let's consider one vessel to be a typical cylinder (the easiest case), and the other vessel a truncated cone (that is, take an upside-down cone, and chop off a smaller cone from the bottom such that the base of the small cone's area is smaller than the area of the base of the large cone).Given that the bases are of equal area and the fluid is filled to the same height in both vessels, it is clear that the volume of fluid held in the truncated cone is greater than that in the cylinder.This gives rise to the question: Why are the forces on the bases equal when there are different masses of fluid pressing on them?Well, you need to consider the walls of the vessel. In the cylinder, the gravitational force of the fluid molecules never contacts the walls, as the force is parallel to these walls. In the truncated cone, however, part of the gravitational force of the molecules not adjacent to the base contacts the walls. This means only a portion of the total volume's gravitational force actually affects the base.As it so happens, you can determine this portion by looking at the column of fluid directly above the base, which happens to be a volume and shape equal to the cylindrical vessel.When you calculate the force on an object at the bottom of the ocean, you can calculate it by considering the gravitational force on the column of water directly above the object, sort of like the cylindrical vessel. The same thing applies to calculating atmospheric pressure and the force of air molecules pushing down on us. You just consider the gravitational force on the column of air above us.
Which tank will be full first? (for this example with four tanks, see question source)
If we add an assumption that the inlet flow of water into the connections and outlet flow through them is same, then for sure both the tanks 3 and 4 will fill simultaneously.For those who understand the law ( Law of gravitational force): The gravitational acceleration is assumed to be same for all the 4 tanks ( and it will always be same for both tank 3 and 4). So at any same height the force acting will be the same. This is the same case for the brim of tanks 3 and 4. Therefore at any flow rate or on any planet, they will fill together, So there’s no doubt in that.In layman language:First the water will start filling in the tank 3 and the vertical connecting tube next to it simultaneously till the time it reaches the open notch of the connecting tube attached to tank 4.Now for every drop of water supplied to tank 3, it will try to raise the level in both tank 3 and connecting tube, but increase in even a single drop will cause the water to flow down into the tank 4. So this will go on until both the tanks fill till the same level of their top level of connecting tube.From here on every drop supplied to tank 3 is shared equally between tank 3 and 4. So they both fill together till they reach brim and overflow.If you still have doubt then this will clarify it for sure.
If a hole is made right through Earth so it reaches the other side, what will happen when one jumps into it?
Earth’s center of mass is pretty much at its core. It is therefore clear that the attractive force exerted by the Earth towards all bodies is directed towards its center.Why is this important? Say the particular hole looks like thisSay the center is at B (it’s not exactly B, but slightly below B). When the person is in the first leg of the journey, i.e. not yet reached the center, he is falling to the center, or basically towards the point of attraction. So, his speed naturally increases.Once he passes B, though, he is now falling away from the center, which is kind of equivalent to jumping up. The force he now experiences is against the direction of his motion, so he now decelerates. Once he completely stops, he falls back towards to the center and the entire cycle repeats.If you’ve noticed, this is basically an SHM (simple harmonic motion). He will keep oscillating about the center with a time period of about 43 minutes (if I’m not wrong).This, however, is assuming that you initially simply dropped into the hole or had low start speed. If you were actively launched into the hole at a high speed, it is possible you may not decelerate fast enough to stop within the hole. You may fly right out the other side. If the speed is high enough, you could even reach space.