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The dimensional formula of energy density is(A) $mathrm{M}^{1} mathrm{~L}^{0} mathrm{~T}^{-2}$(B) $mathrm{M}^{1} mathrm{~L}^{-1} mathrm{~T}^{-2}$(C) $mathrm{M}^{1} ...

Question

The dimensional formula of energy density is(A) $mathrm{M}^{1} mathrm{~L}^{0} mathrm{~T}^{-2}$(B) $mathrm{M}^{1} mathrm{~L}^{-1} mathrm{~T}^{-2}$(C) $mathrm{M}^{1} mathrm{~L}^{-1} mathrm{~T}^{-3}$(D) $mathrm{M}^{mathrm{l}} mathrm{L}^{0} mathrm{~T}^{-3}$

The dimensional formula of energy density is (A) $mathrm{M}^{1} mathrm{~L}^{0} mathrm{~T}^{-2}$ (B) $mathrm{M}^{1} mathrm{~L}^{-1} mathrm{~T}^{-2}$ (C) $mathrm{M}^{1} mathrm{~L}^{-1} mathrm{~T}^{-3}$ (D) $mathrm{M}^{mathrm{l}} mathrm{L}^{0} mathrm{~T}^{-3}$



Answers

The dimensional formula of energy density is (A) $\mathrm{M}^{1} \mathrm{~L}^{0} \mathrm{~T}^{-2}$ (B) $\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}$ (C) $\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-3}$ (D) $\mathrm{M}^{\mathrm{l}} \mathrm{L}^{0} \mathrm{~T}^{-3}$

Okay, So it tells us that the density D is found by divided the mass of an object by its fine so mass divided by fighting. But then we want to know how to get mass in terms of the other variables. Whenever it does give, give something in terms of the other ones, kid something. What's say, X In terms of others, that just means isolate Max. So we just need to isolate the I'm here. So in order to do that, I'm gonna multiply the vive both sides giving us and is equal to B d. So are correct. Answer should be.

What type of quantity do the following units represent? For a No. Leaders represents volumes. Could be centimetres squared, represents area for c millimeters. Cute. Would represent the volume. Mhm. For d milligram per liter represent density. Yeah, for E. Let's go. Seconds would represent time. Yeah, Fresh out nanometers. We represent a length and Fergie Calvin. Mhm represent temperature.

All right, The problem. 1 37 We're going to derive as I units for kinetic energy do two different formulas. So the 1st 1 can Energy is equal to 1/2 him be square and the 2nd 1 is kinetic energy equal to three have pv All right, so for the 1st 1 and is the mess and has a unit of kilograms V is the velocity and velocity has a unit of meat per second So kinetic energy will have a unit off killed ground times, meter per second square and that is equal to kill Graham kilogram Meters squared, divided by second square. So this is the unit derived from the first question. So for the second ones, your P is the pressure and pressure is defined by force. Divided by area force has a unit of Newt. Area has a unit of meter square, so pee and seek war too. This and the ISS the velocity and has a unit of meter per second. So now combining this too The kinetic energy is a quote you unit of the pressure tires unit of the velocity And this will give us new too per meter per second So this is one of the unit. So there is another way. So from here forth, it's also equal to and a were M iss The mess and a is the acceleration. So the unit for acceleration is meter per second squared. It's just the acceleration. Eso no substituting this to here We get the unit of kinetic energy equal to pressure four survived by area force ISS kilogram times meter her second square divided by area and then times the velocity meter per second. So meter, meter, meter, square And we get this sequel to kill Graham her second Cute. So this is another expression for the unit of kinetic energy. So here we get three different s I units, expression for the kinetic energy.

So we look at the coefficient volume expansion of mercury. So that's um This number here, it's called a better, it was 1.8 and seven negative former Kelvin. And the temperature change given is 1 66 Calvin. So we multiply the to uh to get the factional changing volume. That's delta V. Over V. That's a better times a delta T. That turns 3.0 to 9. So now to find the new density, we take the original density and divided by one plus the fractional change in volume. So the idea here is that the volume increases by um a certain factor. So we have to add the factional change to one to get the increase in volume. Um And then we divide the original density by the factional increase in volume. So we know that the mass is constant. Uh for the for the sample of mercury. So if the mass is constant, then the volume and the density university correlated, which means that The volume is the volume increases by .029%. Then the density must decrease by the same factor. So we divide 13,600 by this number 1.29, and this is a new density 13,217 kg from Major Cube.


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