%PDF- %PDF-
Mini Shell

Mini Shell

Direktori : /var/www/html/digiprint/public/site/cyykrh/cache/
Upload File :
Create Path :
Current File : /var/www/html/digiprint/public/site/cyykrh/cache/e5c034625531c039d040e38335710d6a

a:5:{s:8:"template";s:9437:"<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8"/>
<meta content="width=device-width, initial-scale=1.0" name="viewport"/>
<title>{{ keyword }}</title>
<link href="//fonts.googleapis.com/css?family=Open+Sans%3A300%2C400%2C600%2C700%2C800%7CRoboto%3A100%2C300%2C400%2C500%2C600%2C700%2C900%7CRaleway%3A600%7Citalic&amp;subset=latin%2Clatin-ext" id="quality-fonts-css" media="all" rel="stylesheet" type="text/css"/>
<style rel="stylesheet" type="text/css"> html{font-family:sans-serif;-webkit-text-size-adjust:100%;-ms-text-size-adjust:100%}body{margin:0}footer,nav{display:block}a{background:0 0}a:active,a:hover{outline:0}@media print{*{color:#000!important;text-shadow:none!important;background:0 0!important;box-shadow:none!important}a,a:visited{text-decoration:underline}a[href]:after{content:" (" attr(href) ")"}a[href^="#"]:after{content:""}p{orphans:3;widows:3}.navbar{display:none}}*{-webkit-box-sizing:border-box;-moz-box-sizing:border-box;box-sizing:border-box}:after,:before{-webkit-box-sizing:border-box;-moz-box-sizing:border-box;box-sizing:border-box}html{font-size:62.5%;-webkit-tap-highlight-color:transparent}body{font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:14px;line-height:1.42857143;color:#333;background-color:#fff}a{color:#428bca;text-decoration:none}a:focus,a:hover{color:#2a6496;text-decoration:underline}a:focus{outline:thin dotted;outline:5px auto -webkit-focus-ring-color;outline-offset:-2px}p{margin:0 0 10px}ul{margin-top:0;margin-bottom:10px}.container{padding-right:15px;padding-left:15px;margin-right:auto;margin-left:auto}@media (min-width:768px){.container{width:750px}}@media (min-width:992px){.container{width:970px}}@media (min-width:1200px){.container{width:1170px}}.container-fluid{padding-right:15px;padding-left:15px;margin-right:auto;margin-left:auto}.row{margin-right:-15px;margin-left:-15px}.col-md-12{position:relative;min-height:1px;padding-right:15px;padding-left:15px}@media (min-width:992px){.col-md-12{float:left}.col-md-12{width:100%}}.collapse{display:none} .nav{padding-left:0;margin-bottom:0;list-style:none}.nav>li{position:relative;display:block}.nav>li>a{position:relative;display:block;padding:10px 15px}.nav>li>a:focus,.nav>li>a:hover{text-decoration:none;background-color:#eee}.navbar{position:relative;min-height:50px;margin-bottom:20px;border:1px solid transparent}@media (min-width:768px){.navbar{border-radius:4px}}@media (min-width:768px){.navbar-header{float:left}}.navbar-collapse{max-height:340px;padding-right:15px;padding-left:15px;overflow-x:visible;-webkit-overflow-scrolling:touch;border-top:1px solid transparent;box-shadow:inset 0 1px 0 rgba(255,255,255,.1)}@media (min-width:768px){.navbar-collapse{width:auto;border-top:0;box-shadow:none}.navbar-collapse.collapse{display:block!important;height:auto!important;padding-bottom:0;overflow:visible!important}}.container-fluid>.navbar-collapse,.container-fluid>.navbar-header{margin-right:-15px;margin-left:-15px}@media (min-width:768px){.container-fluid>.navbar-collapse,.container-fluid>.navbar-header{margin-right:0;margin-left:0}}.navbar-brand{float:left;height:50px;padding:15px 15px;font-size:18px;line-height:20px}.navbar-brand:focus,.navbar-brand:hover{text-decoration:none}@media (min-width:768px){.navbar>.container-fluid .navbar-brand{margin-left:-15px}}.navbar-nav{margin:7.5px -15px}.navbar-nav>li>a{padding-top:10px;padding-bottom:10px;line-height:20px}@media (min-width:768px){.navbar-nav{float:left;margin:0}.navbar-nav>li{float:left}.navbar-nav>li>a{padding-top:15px;padding-bottom:15px}.navbar-nav.navbar-right:last-child{margin-right:-15px}}@media (min-width:768px){.navbar-right{float:right!important}}.clearfix:after,.clearfix:before,.container-fluid:after,.container-fluid:before,.container:after,.container:before,.nav:after,.nav:before,.navbar-collapse:after,.navbar-collapse:before,.navbar-header:after,.navbar-header:before,.navbar:after,.navbar:before,.row:after,.row:before{display:table;content:" "}.clearfix:after,.container-fluid:after,.container:after,.nav:after,.navbar-collapse:after,.navbar-header:after,.navbar:after,.row:after{clear:both}@-ms-viewport{width:device-width}html{font-size:14px;overflow-y:scroll;overflow-x:hidden;-ms-overflow-style:scrollbar}@media(min-width:60em){html{font-size:16px}}body{background:#fff;color:#6a6a6a;font-family:"Open Sans",Helvetica,Arial,sans-serif;font-size:1rem;line-height:1.5;font-weight:400;padding:0;background-attachment:fixed;text-rendering:optimizeLegibility;overflow-x:hidden;transition:.5s ease all}p{line-height:1.7;margin:0 0 25px}p:last-child{margin:0}a{transition:all .3s ease 0s}a:focus,a:hover{color:#121212;outline:0;text-decoration:none}.padding-0{padding-left:0;padding-right:0}ul{font-weight:400;margin:0 0 25px 0;padding-left:18px}ul{list-style:disc}ul>li{margin:0;padding:.5rem 0;border:none}ul li:last-child{padding-bottom:0}.site-footer{background-color:#1a1a1a;margin:0;padding:0;width:100%;font-size:.938rem}.site-info{border-top:1px solid rgba(255,255,255,.1);padding:30px 0;text-align:center}.site-info p{color:#adadad;margin:0;padding:0}.navbar-custom .navbar-brand{padding:25px 10px 16px 0}.navbar-custom .navbar-nav>li>a:focus,.navbar-custom .navbar-nav>li>a:hover{color:#f8504b}a{color:#f8504b}.navbar-custom{background-color:transparent;border:0;border-radius:0;z-index:1000;font-size:1rem;transition:background,padding .4s ease-in-out 0s;margin:0;min-height:100px}.navbar a{transition:color 125ms ease-in-out 0s}.navbar-custom .navbar-brand{letter-spacing:1px;font-weight:600;font-size:2rem;line-height:1.5;color:#121213;margin-left:0!important;height:auto;padding:26px 30px 26px 15px}@media (min-width:768px){.navbar-custom .navbar-brand{padding:26px 10px 26px 0}}.navbar-custom .navbar-nav li{margin:0 10px;padding:0}.navbar-custom .navbar-nav li>a{position:relative;color:#121213;font-weight:600;font-size:1rem;line-height:1.4;padding:40px 15px 40px 15px;transition:all .35s ease}.navbar-custom .navbar-nav>li>a:focus,.navbar-custom .navbar-nav>li>a:hover{background:0 0}@media (max-width:991px){.navbar-custom .navbar-nav{letter-spacing:0;margin-top:1px}.navbar-custom .navbar-nav li{margin:0 20px;padding:0}.navbar-custom .navbar-nav li>a{color:#bbb;padding:12px 0 12px 0}.navbar-custom .navbar-nav>li>a:focus,.navbar-custom .navbar-nav>li>a:hover{background:0 0;color:#fff}.navbar-custom li a{border-bottom:1px solid rgba(73,71,71,.3)!important}.navbar-header{float:none}.navbar-collapse{border-top:1px solid transparent;box-shadow:inset 0 1px 0 rgba(255,255,255,.1)}.navbar-collapse.collapse{display:none!important}.navbar-custom .navbar-nav{background-color:#1a1a1a;float:none!important;margin:0!important}.navbar-custom .navbar-nav>li{float:none}.navbar-header{padding:0 130px}.navbar-collapse{padding-right:0;padding-left:0}}@media (max-width:768px){.navbar-header{padding:0 15px}.navbar-collapse{padding-right:15px;padding-left:15px}}@media (max-width:500px){.navbar-custom .navbar-brand{float:none;display:block;text-align:center;padding:25px 15px 12px 15px}}@media (min-width:992px){.navbar-custom .container-fluid{width:970px;padding-right:15px;padding-left:15px;margin-right:auto;margin-left:auto}}@media (min-width:1200px){.navbar-custom .container-fluid{width:1170px;padding-right:15px;padding-left:15px;margin-right:auto;margin-left:auto}} @font-face{font-family:'Open Sans';font-style:normal;font-weight:300;src:local('Open Sans Light'),local('OpenSans-Light'),url(http://fonts.gstatic.com/s/opensans/v17/mem5YaGs126MiZpBA-UN_r8OXOhs.ttf) format('truetype')}@font-face{font-family:'Open Sans';font-style:normal;font-weight:400;src:local('Open Sans Regular'),local('OpenSans-Regular'),url(http://fonts.gstatic.com/s/opensans/v17/mem8YaGs126MiZpBA-UFW50e.ttf) format('truetype')} @font-face{font-family:Roboto;font-style:normal;font-weight:700;src:local('Roboto Bold'),local('Roboto-Bold'),url(http://fonts.gstatic.com/s/roboto/v20/KFOlCnqEu92Fr1MmWUlfChc9.ttf) format('truetype')}@font-face{font-family:Roboto;font-style:normal;font-weight:900;src:local('Roboto Black'),local('Roboto-Black'),url(http://fonts.gstatic.com/s/roboto/v20/KFOlCnqEu92Fr1MmYUtfChc9.ttf) format('truetype')} </style>
 </head>
<body class="">
<nav class="navbar navbar-custom" role="navigation">
<div class="container-fluid padding-0">
<div class="navbar-header">
<a class="navbar-brand" href="#">
{{ keyword }}
</a>
</div>
<div class="collapse navbar-collapse" id="custom-collapse">
<ul class="nav navbar-nav navbar-right" id="menu-menu-principale"><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-169" id="menu-item-169"><a href="#">About</a></li>
<li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-121" id="menu-item-121"><a href="#">Location</a></li>
<li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-120" id="menu-item-120"><a href="#">Menu</a></li>
<li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-119" id="menu-item-119"><a href="#">FAQ</a></li>
<li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-122" id="menu-item-122"><a href="#">Contacts</a></li>
</ul> </div>
</div>
</nav>
<div class="clearfix"></div>
{{ text }}
<br>
{{ links }}
<footer class="site-footer">
<div class="container">
<div class="row">
<div class="col-md-12">
<div class="site-info">
<p>{{ keyword }} 2021</p></div>
</div>
</div>
</div>
</footer>
</body>
</html>";s:4:"text";s:15996:"The gravitational intensity at any point is defined as the negative of the potential gradient i.e.,(-dv/dx) At any point inside the spherical shell, the value of gravitational potential is constant implying the intensity is zero. A particle of mass `m'` is placed on the line joining the two centres at a distance `x` from the point of contact of the sphere and the shell. If the two shells coincide into single one such that surface charge density remains same, then the ratio of potential at an internal point of the new shell to shell A … Therefore, the gravitational potential gradient at all points inside the spherical shell is zero [i.e. Newton derived two useful theorems concerning spherical shells of matter. A spherical shell has inner radius R1, outer radius R2 and mass M, distributed uniformly throughout the shell. (C) Inside the shell, gravitational field alone is zero. The zeroth degree term in the spherical harmonic equation agrees with the usual expression for the energy of a radial density distribution. In this problem we prove that the gravitational field inside a thin spherical shell of finitemass is zero. GRAVITATIONAL POTENTIAL FOR NEAR-SPHERICAL GEOMETRIES 231 Fig. Consider a spherical shell of mass m; Newton's first and second theorems (BT87, Ch. At this junction in the lesson our goal to determine what the gravitational force would be on a point mass, m, if the point mass were to be placed (1) outside of a thin spherical shell, (2) inside a thin spherical shell, and then (3) inside a solid spherical mass. 2.1) imply the acceleration inside the shell vanishes, and the acceleration outside the shell is - G m / r^2. In classical mechanics, the shell theorem gives gravitational  simplifications that can be applied to objects inside or outside a spherically symmetrical  body. I wanted to try a different approach than they did. Thus B,C,D are correct. 2. Relation to the integral form. Newton’s first theorem: A body that is inside a spherical shell of matter experiences no net gravitational force from that shell. So the potential inside of a spherical shell is constant, \[ \begin{aligned} \Phi(r) = -\frac{GM}{R}. Consider a spherical shell of mass m; Newton’s first and second theorems (BT87, Ch. 3 Gravitational Potential Energy Recall that our previous expression for gravitational potential energy near the sur-face of the earth is U = mgy. The same pair of results applies in electrostatics, since that is also an inverse square law. Because the force is given by F r =  … Consider a thin uniform spherical shell of the radius (R) and mass (M) situated in space. \Proof" Calculate the potential at point p~ at radius rfrom the center of an in nitesimally thin shell … The gravitational potential at the centre increase or decrease explain? Outside the spherical shell. 2013). Both of these can be proved using simple calculus, and were first shown by Isaac Newton. Gravitational potential energy cannot be calculated but the change in gravitational potential energy can be calculated. This is done by choosing so... A hollow spherical shell is compressed to half its radius. (1) A body inside a spherical shell of matter experiences no net gravitational force from the shell. Here it is Is it a wave, a constant or something undiscovered? Intensity of gravitational field inside the hollow spherical shell is. Gravity Force of a Spherical Shell. Orbits in spherical potentials¶ “Orbits” are the trajectories that bodies travel on under the influence … A uniform shell of matter exerts a force on a particle located outside it as if all the mass was at the center. The gravitational potential of two homogeneous spherical shells A and B of same surface density at their respective centers are in the ratio 3:4. Page 10 of 27 The total mass of the shell is M. With- out a complicated mathematical analysis that involves integration, show that the total gravity on any test mass inside the shell is zero!!. Related Papers. This infinite potential suggests that there will be difficulties when we attempt to evaluate the same physical situation in the context of general relativity. 2. The above-mentioned shell theorem explains how to calculate the gravitational field inside and outside the shell. Let's take a very small part of it and pull it out to infinity. A 3D object divides space into 3 parts: Inside the spherical shell. r m 2 m 1  Hence in any two directions: δm 1 /δm 2 = (r 1 /r 2)2 δF 1 = - δF 2 Gravitational Potential of a Spherical Shell. Log in. The gravity at the centre of a perfectly formed sphere in space will never be ascertained until we have found out what gravity really is. Graph of the electric potential as a function of the distance from the centre of the shell: The electric potential inside the hollow part of the spherical shell is constant and is equal to \[ \varphi (z)\,=\,\frac{\varrho}{2 \varepsilon_0} \left(b^2-a^2\right)\,.\] The electric potential inside the charged spherical shell is equal to On the surface, this is the same. The … Gravitation. Newton I: The net gravitational force exerted by a spherical shell of matter on a particle at a point inside the shell is identically zero. Spherical Shell Gravitational Potential : © 1996-2007 Eric W. Weisstein Anywhere within the shell. The gravitational potential at a point is defined as the potential energy of a unit mass at that point (). Consider a point mass M, the gravitational potential at a distance ‘r’ from it is given by; V = – GM/r. Consider a thin uniform spherical shell of the radius (R) and mass (M) situated in space. Now, As E = 0, V is a constant. The value of gravitational potential is given by, V = -GM/R. The field inside the sphere is zero only if there are no other masses present. We see that the shell may be treated as a point particle of the same mass placed at its centre to calculate the gravitational field at an external point. It is a result of the Newton’s Shell Theorem. In simple language we can assume that all the mass is uniformly distributed on the outer edges of the... R ! The field is zero and same everywhere inside a shell, so (b) and (d) is true. Eq. The shell theorem, proved by Newton in his Principia (1687), states that the net force exerted by a uniform spherical shell on a body located anywhere inside it is zero, as long as the force is proportional to the inverse square of the distance between the interacting bodies. Second Theorem The gravitational force on a body outside a closed spherical shell of matter is the same as it would be if all the shell’s matter were concentrated into a point at its center. We know, as you calculated, the self potential energy in this case becomes 1 2 M 2 R. But things change when we go inside the shell. as V is constant, dV/dr = 0]. 1. The gravitational potential at the centre (A) increases (B) decreases (C) rema. COMEDK 2000: A hollow spherical shell is compressed to half its radius. A particle of mass M is at a distance a from surface of a thin spherical shell of equal mass and having radius a. Fig. Physically, this is a very important result because any spherically symmetric mass distribution outside the position of the test mass m can be build up as a series of such shells. This is equal to the potential energy of two point masses m and M at a distance r. So we have proved that the gravitational potential energy of spherical shell M and point mass m at any distance r is the same as though they were point masses. Hence, intensity is also zero at all points inside the spherical shell. The first term on this equation reproduces the potential generated by a spherical shell with variable density ρ(r′) = ar′, while the second term constitutes the potential generated by a spherical shell with homogeneous density ρ = b (Mikuška et al. Consider the cones originating from the point P intersecting the spherical uniform shell of matter at derivation of V=-GM/R & E=-GM/r2 due to spherical shell outside , on surface & inside the spherical shell. This applies only to spherical shells of uniform density, which happily is a condition well met by stars and many other objects. Concept: Universal Law of … So, intensity at all points inside is zero. Again, base your analysis on a figure and intuition. A solid sphere of mass `m` and radius `r` is placed inside a hollow thin spherical shell of mass `M` and radius `R` as shown in the figure. The gravitational self-energy of a spherical shell. STATEMENT -1 : Gravitational field inside a spherical mass shell is zero even if the mass distribution is uniform or non-uniform. 11748523 193.0k+ Gravitational Field of a Sphere Side 3 Uniform Spherical Shell To calculate the gravitational attraction between an object of mass m and a spherical shell of mass M and radius R a distance of r from the mass, we will divide the shell into a bunch of rings, and simply add up the force between each ring and the mass. The mass contained in the shell is Thus, the minimum value of (1) will be when all the charge is at R = 1. That is, F grav= 0,r<R − GmM r2 e r,r≥R ⎧ ⎨ ⎪ ⎩ ⎪ (5.4) with e r the unit vector directed from the centre of the shell to the mass. Inside the shell, the gravitational potential is same throughout, it doesn't change at all, and hence, since it doesn't change however small we move about, from the above equation, we … Join now. Thanks for the A2A. Considering Earth as a uniform solid sphere of mass M and radius R The potential at any internal point at a distance r from the... An object is located inside a thin, uniform density spherical shell. to define quantitatively what we mean by the strength of a gravitational field, which is merely the force experienced by unit mass placed in the field. When the body moves away from the earth, r increases, the gravitational force does negative work, and U increases (i.e., becomes less negative). Now let us consider the potential for a particle inside such a shell. Newton’s Shell Theorem A uniform shell of matter exerts no net gravitational force on a particle located inside it F=0 A uniform spherical shell of matter attracts a particle that is outside the shell as if all the shell’s mass were concentrated at its center. Ask your question. Sample Problem Three explorers attempt to travel by capsule through a tunnel directly from the south pole to the is infinite everywhere. A body that is inside a spherical shell of matter experiences no net gravitational force from that shell. Newton’s second theorem: The gravitational force on a body that lies outside a closed spherical shell of matter is the same as it would be if all the shell’s matter were concentrated into a point at its center. To see why, consider again the case of a spherical shell of mass in the limit as the shell's radius increases to infinity. StudyAdda offers free study packages for AIEEE, IIT-JEE, CAT, CBSE, CMAT, CTET and others. The magnitude of the gravitational force exerted on the shell by a point mass particle of m, located a distance d from the center, inside the inner radius, is: (Gravitation due to a Spherical Shell… Draw vector diagrams to back your reasoning. 13.5: Gravitation Inside Earth: Shell Game II 1. 4. Our previous examples have paved the … Title: Microsoft Word - celm05.doc Author: jtatum Created Date: 1/28/2020 8:53:35 AM This theorem has particular application to astronomy. But we know, according to Gauss's law, that the charge gets distributed in the form of a spherical shell on the surface of the spherical ball. i.e., where r is the distance of point from source mass M. I shall use the symbol g for the gravitational field, so that the force F on a mass m situated in a gravitational field g is F = mg. 5.2.1 It can be expressed in newtons per kilogram, N kg-1. 2. For example, the gravitational force felt by a mass m located at a radius r inside a spherical shell of radius R and mass M (i.e., with r≤R) is zero. Quasilocal energy for a Kerr black hole. Case II: P is outside the shell, r > a. E = GM/(4ar 2)[z+(a 2-r 2)/z 2 ] (a-r) (a+r) = 0. Thus we have the important result that the field at an external point due to a hollow spherical shell is exactly the same as if all the mass were concentrated at a point at the centre of the sphere, whereas the field inside the sphere is zero. Where a = radius of the shell. Potential due to uniform spherical shell of mass ' m' and radius R at a point inside it is - 28048342 1. I thought this would be easy but cant reproduce the answer in Marion,Thornton 5ed,p188. Total: 5 2. Now, Case 1: If point ‘P’ lies Inside the spherical shell (r<R): As E = 0, V is a constant. (c) the gravitational potential is same everywhere (d) the gravitational field is same everywhere. The gravitational potential gradient is equal to the negative of gravitational intensity. Outside a uniform spherical shell of mass the net gravitational force is the same as if the shell were collapsed to a single point at its centre. 2006; Grombein et al. Inside a uniform spherical shell, the gravitational field is the same everywhere and is equal to zero. Figure %: Particle m inside thin shell. The field is zero and sameeverywhere inside a shell, so (b) and (d) is true. Figure 13.11 shows how the gravitational potential energy depends on the distance r between the body of mass m and the center of the earth. A particle of mass M is situated at the centre of a spherical shell of same mass and radius a.The gravitational potential at a point situated at a/2 distance from the centre will be -3 GM/ a -2 GM/a When considering the gravitational force exerted on an object at a point inside or outside a uniform spherically symmetric object of radius [latex]\text{R}[/latex], there are two simple and distinct situations that must be examined: the case of a hollow spherical shell, and that of a solid sphere with uniformly distributed mass. If you are referring to a sphere on the surface of the earth, the the gravitational potential would be down towards the surface from its center of mass. If you mean a sphere in space, like the earth the gravitational potential would be zero because it has even mass at every point around the center. Writing doesn't have to be stressful. This indicates that gravitational forces acting at a point in a spherical shell are symmetric. Gravitational attraction and potential of spherical shell with radially dependent density Roland Karcol 1 nAff2 Studia Geophysica et Geodaetica volume 55 , pages 21–34 ( 2011 ) Cite this article Figure 3: Thin walled, spherical shell with radius a observed at point P. From Blakely Therefore the gravitational potential at any point outside a uniform shell is equivalent to that of a point source of the same mass located at the centre. Modeling the motion of a simple harmonic oscillator; gravitational field of a spherical shell of matter; gravitational force inside uniform sphere. Figure 3 shows a ring on Both types of forces, electrical and gravitational, are very similar. (B) Gravitational field is zero not only inside the shell but at a point outside the shell also. 13.5: Gravitation Inside Earth We stated before that a uniform shell of matter exerts no net gravitational force on a particle located inside it. (A) Gravitational field and potential both are zero at centre of the shell. r F V ins= 4π 3 r3 m V … ... so that the remaining mass still forms a spherical shell. 12. The net gravitational force on a point mass inside a spherical shell of mass is identically zero! Physically, this is a very important result because any spherically symmetric mass distribution outside the position of the test mass m can be build up as a series of such shells. Gravity does cancel out for all points inside a hollow spherical shell. That is, assume there is no air inside a soccer ball, the gravity from the... For a solid sphere, the force on a test mass INSIDE includes only the mass closer to the CM than the test mass. ";s:7:"keyword";s:51:"gravitational potential inside a spherical shell is";s:5:"links";s:746:"<a href="http://digiprint.coding.al/site/cyykrh/laroyce-hawkins-snapchat">Laroyce Hawkins Snapchat</a>,
<a href="http://digiprint.coding.al/site/cyykrh/who-covid-19-updates-pakistan">Who Covid-19 Updates Pakistan</a>,
<a href="http://digiprint.coding.al/site/cyykrh/what-is-locus-roblox-username">What Is Locus Roblox Username</a>,
<a href="http://digiprint.coding.al/site/cyykrh/caroline-gill-the-memory-keeper%27s-daughter">Caroline Gill The Memory Keeper's Daughter</a>,
<a href="http://digiprint.coding.al/site/cyykrh/charge-to-mass-ratio-of-an-electron-lab-report">Charge To Mass Ratio Of An Electron Lab Report</a>,
<a href="http://digiprint.coding.al/site/cyykrh/top-neurosurgeons-in-massachusetts">Top Neurosurgeons In Massachusetts</a>,
";s:7:"expired";i:-1;}

Zerion Mini Shell 1.0