Physics-
General
Easy
Question
From the previous question in the reference frame attached to the center f inertia, the total kinetic energy of the two particles is
The correct answer is: ![1 half open parentheses fraction numerator m subscript 1 m subscript 2 over denominator m subscript 1 plus m subscript 2 end fraction close parentheses open parentheses v subscript 1 superscript 2 plus v subscript 2 superscript 2 close parentheses](data:image/png;base64,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)
Related Questions to study
physics-
A closed system consists of two particles of masses
and
which move at right angles to each other with velocities
and
. In the reference frame attached to the center of inertia, the magnitude of momentum of each particle is
A closed system consists of two particles of masses
and
which move at right angles to each other with velocities
and
. In the reference frame attached to the center of inertia, the magnitude of momentum of each particle is
physics-General
physics-
A man of mass m is standing on a platform of mass M kept on smooth ice. If the man starts moving on the platform with a speed v relative to the platform, with what velocity relative to the ice does the platform recoil?
![](data:image/png;base64,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)
A man of mass m is standing on a platform of mass M kept on smooth ice. If the man starts moving on the platform with a speed v relative to the platform, with what velocity relative to the ice does the platform recoil?
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)
physics-General
physics-
A boy having a mass of M kg stands at one end A of a boat of length dm at rest. The boy walks to the other end B of the boat with a velocity u relative to the boat. What is the velocity of the boat? Friction exists between the feet of the boy and the surface of the boat. But the friction between the boat and the water surface may be neglected. Mass of the boat is 4 m
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)
A boy having a mass of M kg stands at one end A of a boat of length dm at rest. The boy walks to the other end B of the boat with a velocity u relative to the boat. What is the velocity of the boat? Friction exists between the feet of the boy and the surface of the boat. But the friction between the boat and the water surface may be neglected. Mass of the boat is 4 m
![](data:image/png;base64,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)
physics-General
physics-
A equilateral triangular, square and circular plates of same thickness and made up of different materials are arranged is shown in figure.
The ratio of their respective densities are
. The centre of mass of the arrangement lies
A equilateral triangular, square and circular plates of same thickness and made up of different materials are arranged is shown in figure.
The ratio of their respective densities are
. The centre of mass of the arrangement lies
physics-General
physics-
The centre of mass of a triangular lamina of uniform density of height h is
![](data:image/png;base64,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)
The centre of mass of a triangular lamina of uniform density of height h is
![](data:image/png;base64,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)
physics-General
physics-
A semi-circular plate of radius R has density
, where
is the distance from centre. The position of centre of mass from 0 is
![](data:image/png;base64,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)
A semi-circular plate of radius R has density
, where
is the distance from centre. The position of centre of mass from 0 is
![](data:image/png;base64,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)
physics-General
physics-
A semi-circular plate with cavity having inner radius R and outer radius 2R with uniform density is a shown. The centre of mass of the thin plate is at
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FI8PJLEKfQPu4Q2VDhZaqoL5DbYnMUG6rjQKJFi5B+0qRJVqxYMTc7yRcoBODHIsqSgTQ8Jk+e7PxbGzdujE5ST//+/V1jfRzaexItWqxgYsKnb/d98le0iWBeFOFBZMy4a9ppfLkmEm1xo2DXY+gkVrSIZpjigDiQi/AFRs1gu2CllQgXrok0Lo8ePTo6ST1E71ShQ89tJVa08NZgvBs/fnx0knp4QtN+wXQJZr2HBI3DGGARXfFD6oEOBgo8vjS104vIeyt0l3wiRYuQnXadsmXLeuUWnj59uov8QlxIQYWqQIECrqPAxxaoVMD8rebNm7uJHD6YThFSIniurSG75BMpWqyyL1GihNsU7Qs0auNeZh55aBAV5s+f3/LkyeNeOLCTtNLqYrDFiWuiL6ZTJpeQxw3Z95c40SLKwiXMaBfc5j7A90G+AS9NiBNIuXbky5fPCdY111zjJqnGrd/tSuHazLYcX95vjA1v3bq1NW3aNDoJj8SJFm5l8gxsEvaFpUuXushv7ty50UlYMPb5hhtuOCtaTHtVpPUjmIQrVarkTS6JKSEUe1asWBGdhEWiRItfJHJZbNehO98HiKx46hGdhAr5Gvojr732WitYsKArr4sfIbofMGCAi6R9qFSf2ePZpk2b6CQsEiVa7IcjoqFtxxd4+mJu9alf7UrAwc9ChWXLlkUn4qdggSCXNHz48OgktYwZM8bZH3ze5XkhEiNaVE7wZfG082UTL7YL3jj9+vWLTkRc4f03ePBg9/7zofuChwyTTbt27RqdhENiRIv2Bao4TE3wofzMlQF3Ml4xH7e6iOyHhnwqxIiXDwwcONC55H2buvprJEa0ECsE4sCBA9FJajmzo06tOsmBhyV+NnoAiXRSDX46zKbk20IiEaJF0h0j6dixY72Isvh+mJJK570vvWkidzgz38qXsdm8D9lKTQU4FBIhWiTeGYdLg7QPZGVlWeHChYN0vourg9wWOUzW6/swcWHr1q3O/kBiPhRiL1q8SZivzv2d/51qaFbNyMhwg+JEMsG3RW4L+40PtGvXztlufLiyXgqxFy3aKIoUKeJNaZdZ4oUKFfJq1lKOc/p7O3H8Gzt67KT5s/YhdfDwZPUYD1MfOgeI/In8QllNF3vRomWByQk+TP8kymIWPRuiE8Hx3fbu8A5Ws9Rt9rd8N9gN+f5uaaUfsWdHvWd7/Nomn+vgZyO35YNnEBEl0sJsGkL7VaxFixwWG1KIbnxgyZIl7vsJrcR8RXy7w95qU9L++/d57foby1n9lhnW/slHrMyNf7Z/uy6fVWo3ybYluNOHAkyrVq2cM90HWKVPJTGEzeWxFi0WQjBj3QebA14sZr537949OokzJ+xAZlu76d//1f54Z7rN3vqlHT3+nX137KgdWDPF2hX5reX5053Wfuqe6M8nE+wuXBFJYaQaWtxIyNPc7TuxFS1sBTRG88bwweawcOFCVzH0pYKZo5z4wjJb5Lff5f0fqzXq3Pako7Z2XD27Ps/vrVKLSdFZMqF6yIPMl3FE2B9atmzp/Ty02IoWPX0MpPPhKkY+jYivZ8+eXlQwc5rTx/baqw/82a770x3WNevcHMlp2/1+byv8m3+xcjX8f6rnNGdc6cxTSzVMfeCKyAPWZ2IpWggDoS5zs3wwbxL+p6WlueGDieD4Xhte9a//EK1C1vmDc0Xre9v13gt26z9fa+VqDYzOkgtV5Fq1atnIkSOjk9TBjYS5XzjkfbidXIhYihamTVpkVq1aFZ2kDobAEXJ37NjRm6GDOc7Jr21RRpr97rd/tSqvbLGfPzYOW9ZrVe0Pef5o96b7M20jlbRt29aNZOa9kmqwYvB+ZR+or8RStFq0aOHmO/ngOKZt49Zbb7XVq1dHJ0nglH2x9Dm76z+vtbz5H7XRWZ/ZwcNH7OvDB2zbu8OsUf7f2D/9VynrkhnelNacYMGCBc7+sGjRougkdfCg55ayePHi6MQ/YidaDNUrWrSoF1NACbFZJIA3K3Fbok/us4W9qtrf/3Kd/cf/plnFmvWtXo0KVuj//mDX/eUWq90j08LpdstZiLDq1q1rnTt39uJaxpRVUiu+XhFjJ1ps0iXp7UOVjhAb9zv+rERy+rB9PP0la1mzvN1V6FZLu6Ok3V8/w17L3GB+TDTzB8YUsSVn27Zt0Unq6NWrl9dXxFiJFm5exs/4Mh2S3jImOfi0cl/4Cfsiqdz58N5dv369G1bo6xUxVqLFlZAeKrbDpBoEtHz58jZu3DgteRCXBA55Ugk+7C/gijhkyBAv37uxEq2GDRs6F7wP0FtWunRpLS4VlwyJeCJzH9IJbFRCQH3wj51LLEQLAykd6mw47t27t1vPjmik6sXX581HcpVeLh9K2cJ/iM5p62EHZqphoxIz6HzsRYyFaI0fP96NsK1QoYITChLxtEek4kW0x7KKvHnzulVlHTp08GaRhvAffFJNmjTxIkLnisiEVd+m68ZCtHbu3OkWnhLlMNGBpwP/nYoXX59xOLRmzJ492/leNFJZXCr4+sjLTp8+PTpJHTjjGVbp2xUxVjktX0C8EjXkT2QrrPbq1q1bytMKtJ2VLFnSm9FOZ5BoCeEZNPuTavCh2Z/cLH2RPt0WJFpCeMb8+fPd1vH09HS3cGLUqFEpeY0ePdpNSuHl07YeiZYQnoH1AUc6TdTklJo1a5aSF1+botb111/v1eYoiZYQnoG5lMgGl3yqXxS5KAzg2/LB9AoSLSHERcnMzLTatWt7s9tAoiWEuCiYXrER+eI3lGgJIYJCoiWECAqJlhAiKCRaQoigkGgJIYJCoiWECAqJlhAiKCRaQoigkGgJIYJCoiWECAqJlhAiKCRaQoigkGgJIYJCoiWECAqJlhAiKCRaQoigkGgJIYJCoiWECAqJlhAiKCRaQoigkGgJIYJCoiWECAqJlhAiKCRaQoigkGgJIYJCoiWECAqJlhAiKCRaQoigkGgJIYJCoiWECAqJlhAiKCRaQoigkGgJIYJCoiWECAqJlhAiKCRaQoigkGgJIYJCoiWECAqJlhAiKCRaQoigkGgJIQLC7P8B7SdzNOXPd6MAAAAASUVORK5CYII=)
A semi-circular plate with cavity having inner radius R and outer radius 2R with uniform density is a shown. The centre of mass of the thin plate is at
![](data:image/png;base64,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)
physics-General
physics-
A rod AB of length 10 cm, has its mass per unit length varying from 1 kg/m cat end A ) to 2Kg/m ( at end B). The distance of centre of mass from end B is :
![](data:image/png;base64,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)
A rod AB of length 10 cm, has its mass per unit length varying from 1 kg/m cat end A ) to 2Kg/m ( at end B). The distance of centre of mass from end B is :
![](data:image/png;base64,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)
physics-General
physics-
If a square of side R/2 is removed from a uniform circular disc of radius R as shown in the figure, the shift in centre of mass is
![](data:image/png;base64,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)
If a square of side R/2 is removed from a uniform circular disc of radius R as shown in the figure, the shift in centre of mass is
![](data:image/png;base64,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)
physics-General
physics-
If a triangular sheet is removed from one edge of a uniform rectangular sheet as shown in the figure, then the shift in the centre of mass of the system is
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)
If a triangular sheet is removed from one edge of a uniform rectangular sheet as shown in the figure, then the shift in the centre of mass of the system is
![](data:image/png;base64,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)
physics-General
physics-
The co-ordinates of centre of mass of letter E which is cut from a uniform metal sheet are (Take origin at bottom left corner and width of letter 2 cm every where)
![](data:image/png;base64,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)
The co-ordinates of centre of mass of letter E which is cut from a uniform metal sheet are (Take origin at bottom left corner and width of letter 2 cm every where)
![](data:image/png;base64,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)
physics-General
physics-
Two blocks of equal mass are tied with a light string which passes over a massless pulley as shown in figure. The magnitude of acceleration of centre of mass of both the blocks is (neglect friction everywhere)
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)
Two blocks of equal mass are tied with a light string which passes over a massless pulley as shown in figure. The magnitude of acceleration of centre of mass of both the blocks is (neglect friction everywhere)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUEAAACNCAYAAAApU8hKAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AAC/uSURBVHhe7Z0HmBPl2oY9en7P8RyqAtKkLdKsFBGPNEHpvUmXLs2V3pSiAqIgRVRAUWyIKCBVEKQoIkUBpUsVadJBQKTI++/97QxkQzKzyya7yea9rysXbDI7yWZmnnn7d5MoiqJEMCqCiqJENCqCiqJENCqCYciFCxdk165dsmrVKvniiy/k3XffNY8ZM2aY53iNbRRFcUdFMIw4ffq0LF26VLp16yb333+/ZM6cWe644w656667zIP/33nnnfLAAw+YbRYvXix//PGH9duKovhCRTBM+PHHH6VZs2aSLl06yZ8/vzRp0kSGDx8uc+bMke+//948+D/P8VqBAgUkbdq00qJFC/nhhx+svSiK4o2KYBgwefJkyZkzp3kMGDBANm3aZL3in61bt8rAgQPN7+TOnVvef/996xVFUTxREQxxJk6cKP/+97+lQoUKsmLFCuvZ+MPvVKxYUW677TZ58803rWcVRbFREQxhpk6dKv/973+lbt26cuTIEevZhPP7779Lw4YNJVWqVDJlyhTrWUVRQEUwRMGdvfvuu6Vs2bJy8OBB69m4nDp1ymSHR44cKcOGDZPRo0fLggULfGaGEUL2xT63b99uPasoiopgiNKqVSvJlCmTTxf40KFDRvjKlSt3NTucJ08eky3mUbVqVRk3btx1meHVq1dLtmzZpHTp0jJ27FjrWUWJbFQEQxAywQhgr1695O+//7aejWXHjh3yxBNPGDe5UqVKMn78eFmyZIl89913snDhQiOOjzzyiPznP/+Rxo0bG8H05Pnnn5ebbrpJ/u///k+effZZOX78uPWKokQmKoIhSNeuXU2939q1a61nYkEAS5YsKRkyZJCPP/5YDh8+bL0Sl71795pSmTRp0kjNmjXlwIED1itiXOEcOXJI9uzZjRiSNKHAWlEiFRXBEOOvv/4y7mqNGjXk5MmT1rMif/75p3kOC3Hu3LnWs/65cuWKvP3226ZWEFE9e/aseZ7916lTR0qUKCGTJk0y+8uVK5fpOFGUSERFMMSwEyKDBw82QmazaNEiUyj96quvWs+4c/nyZWnXrp2xKu3aQtzrl156SfLmzWssSeKEWJdYjX379pWLFy+a7RQlUlARDDH69+9v4nUzZ860nhG5dOmSNG/e3AiXd4zPjZUrV5pkyJAhQ8x+gB7jrFmzGmEFss+dO3eWf/3rX6Yc55dffjHPK0okoCIYQhADvOeee0ysjmSHDTWCdH506NDBeuZ6EDgsP2+w/KpUqWKsvaNHj5rn6D8mi/zZZ5+ZnwF3+/XXXzcJFVruaMHztEQVJaWiIhgiIGJYYzfffLP84x//uGqlAZYZ1tyYMWOsZ65B3HDatGnSpUsX484int51gp06dZL77rtP9u3bZ37+6quvjCU4a9Ys87MNosdrDGBInTq1jBgxQs6fP2+9qigpExXBEAH3l7hcmTJlTN2fZ6/vli1bjAi+9dZb1jOxII7VqlUzgoV44kbz/wkTJsQprUEgCxUqdFUE6RpBBJctW2Z+9mbPnj1XO0xat24tv/32m/WKoqQ8VARDgHPnzplYHJla4nWlSpUyVqFthRGzQxh79+4dx+WlQwTxI/HBv5TO3HLLLfLkk0/KsWPHrK3E/FysWLGrz2EZEl/0LJ3xhvcZNGiQpE+fXooUKWJcaEVJiagIhgAUPBMHfPnll83PlLAULVpU9u/fb36mrKVy5cpGuBioYAvhO++8Y34P8evRo4ex3vgZ69D+XcZoURdImQxu8k8//WSyz4zbig9Yjfny5TOxwvfee0/dYyXFoSKYzOCiUrNHHM7u6X3jjTeMa+yZISbuh8Bh9dn1gwgUz0VFRcn8+fPNmC1+JgmCS8sDK44YI/MGf/31VylYsKDceuutcfbtxoYNG4ywsu+ePXv67WVWlHBERTAZoSbvxRdflH/+859xipUZdoD7+thjj8m6detMwoKp0ogdcTo7aTJ9+nQjaBkzZjSxQOJ8jMxCUInjke1FuCiyPnHihBFSBBHX2rMQOz7gstNmR9yRsV5r1qyxXlGU8EZFMBnBNUW4qlevHieGB8z+Q8AQQ8pXAHeU57AcEVDidFiGiBLPt23b1rjE7BO3mRH8tMfZ7XeNGjUy21EzeKPlL3wu3Gvil4iqooQ7KoLJBBNe2rdvb7pAcGW94XUGJSBaxP6AWCC/w5BVagaJ8yF41AFiTVLSQrE11iHbMIafUVuAC0uSgzrExK47QlaZ1j4+G3HMhFqVihJKqAgmE19//bURkaeffvq6STE2TIZhVBZCaVtdJDdoe8PKoy84S5YsZkgCSRPqBBFJ9suEGeKAwKQYrEDcZlsUEwuZ5ZYtW5r3wvokbqgo4YiKYDKA64uVR2zOTTwog0FocD89F0xChBikitXXvXt30+FBPeHQoUPN9gxXRVwRTyxFLMNRo0YFtAsEyxRLkCTOvffeG6/BDooSaqgIJgOMwUKoSIq4gZCR4KAMhlIVBiIgjCy+xJAFEh3E+GwolWHfDFzFGrQFiokywWqDmz17tslC817EDD1rGRUl1FERTGKw4IjVIRoJKTVhDeGOHTsaISQOWLhwYZMQwRLs16+ftZWY+j9EkLq++vXrm6wzFmKw2bZtmynK5r1x8SnHUZRwQEUwCaHoGeuPMhNm+SUU+os3btxoBPHbb781rXV0iFC6snPnTtm9e7cZpoow8qAFj9FcSQVlOMQlSdKQ1fbXlqcooYSKYBJCMTRJDuKB1N0lFmr1qAusVauWWZOEYulPP/3U1BLSekf5DAkTeo79JV8CDa4wrjplNDx0vWMl1FERTCKY7Ny0aVOT7Q2UhcSsQOJwxP4Yk0+WFhG0J8BQh0hJjL3eiN1KlxSQ8EHs+Xz0PGMlKkoooiKYRFDuwtBSprIEChZkovavXr16plCanmOywcwKtCdQE5vjPYnVIYgsxpRUMLmaOCbuMYkaXHlFCTVUBJMAWt5YAQ73cNeuXdaziQdri0QJ4vfUU0+ZmYGIIe/j2RVy5swZ+eijj+T22283ligrztlrjgQb3H7ccYSZmkZKeRQllFARTAI++OADU6dHSUsgIfaGlUWckRIaiqf5F6FDBL3jgKwzwnAF4oj0JSdV0gQxZkU7JuPwGalvRJgVJRRQEQwyjMZnNTesNCzCQMFAVRZc58HUGaZEE2ukT5jpMf5EhtgcliDJE0ptSFzYvcnBhvH+lO3w3livgbSKFeVGUREMMiQFWCjdcz2PxIJlRescpTYUQScULEQ6SphKgyVJzJDJNUkBgx+wiLFYef/ly5dbryhK8qAiGEQoIMY1pajZe92PxMB4LZIszPhLTOkLi7RT4Ixl9uCDD5raQ3tFumDz5ZdfmtmGuOYUdKt7rCQXKoJBhJH5xMA8e34TC5YUXSGIK0XTiQXRo9WNkVuU0tALbK9KF2xw27lBYI3SZaJrmSjJgYpgkGDVNiwsSkQCuaC5PX0mkKU2wMSZ//3vf2bfxOuSotUOGNdPxws3i+LFi8v69eutVxQlaVARDAKUhVASQ0lIIK0bXEaEInfu3LJjxw7r2cDBdBtimGSbSbiQfabVLymghIe1T7BwqXUM5I1DUZxQEQwCuJe4eKwTHMiJKgxXZWoMSZFgMnXqVDN5BqswOjraxA6TAjLbtPuxch49yIcOHbJeUZTgoSIYYOjQoICZdT4YZhoomDhD3I7pM4mdDB0ffv7556sTacqXLx+Q+GN8oMuEYa0MhmAOorrHSrBREQww9jw/6vYCCau8URKDlZZUEK/DqqWchW4TipyToqaQZM3YsWPNAIgCBQqYTLKiBAsVwQCyevVqMwG6du3aAS35wCqjR5i1h5NjYClJHntNEYY00HmSFCxZskQeeughMxDilVdeSbKibiWyUBEMIAgE1hotYoGEUhsKrgO934TArMI+ffoYIWSgK9OxkwI6Y+gyIRbKoAjKahQlkKgIBojPP//cCBXuMG5koGCRdAqKO3XqZD2TfNCpgjvOgAY+U7du3eTUqVPWq8GDVj+6TLjBYBlS1K0ogUJFMABQWsJAAspK6BIJFLi+1O4RG8MSCxXoWMHqxSpkZuA333xjvRI8EGBig5QHIcLjx4+/OiVHURKDimAAYCEkSmII5gcyZsdgVMpF2H+ogfCz4BOfD1Gy5xcGG4q4H3/8cWOJtmnTRtc8VhKNimAiYaYfCycxNJTyjkDBFOhChQqZ+BuTaEIVOlgYkUUvc7NmzZKkppD6QcIOrKNSokQJHdaqJAoVwUTCSm+4hYEuXencubOxsgJdahMM6Irp2rWr+R5YFN5eKD6YEHdlKQFKd7BEk7J0SElZqAgmAqwgkiEtWrQI6JQYRvEziZmsaFIURgcCyldofcuYMaPpAyaTHIjFpNygfIjCdFr9qKUMZFJKiQxUBG8QRI/OBoYkUM8WKCgUZrwVrh5DDcINOjyqVq1qJtKQNGEdlGCDe8zyAhwLaimTckEpJfxREbxBcMVIhmDxBHI5S6wpBPC5555Lstl+gQYLkPWVKXKm24Se52AXOmMBMmEbK5QYLTem5CgsV8IPFUEfkPlkjWB/CQmmMJMIYSjo5s2brWcTD64vfbqMvU+qUVbBgvKVefPmmWGt9rxA+qqDzdKlS02pErFCMtbhEk5Qkg8VQS+wvho1amSC/A8//LBJTHjX6GFxULhLiUggGTp0qHlfauBSCgx+oJQFV5UlPxHGYFtodJVUr17dZKxZ6/nAgQPWK4pyPSqCXsyYMcO4cZReME4KKyZnzpxmLBalGHQrYGlwkQVySszOnTtNZvXRRx9NkROWuXHwPSLy9AEHu+yHJUVxyZlPyM1szZo11ivxB2tW5xqmfFQEPeCkp/ODDCcuLw9cqkqVKpkLGPHjguJCHjdunPVbiYckC9OVWZaTNrmUCr3PJE34/hgycSPClFCmT58uefPmNceURanimz3GjaZY/YUXXtDFoFI4KoIeLFy40ExrYUlKT7gIyDpy8dqPGjVqmBXkAjHhmbYzEgjM70uKXtzkhKQJA1NJYCBMrMkcyPIiXzCstWzZsqbukiGx8RnWihVpH2vOiddee02HvKZQVAQ9qFmzpunTJTGCFYgV0atXLyNQuMgIIWuGEOSnS4ILhMD/yJEjZeXKldZeEgbDARo0aGBGcFEfGCmQXS9WrJj5Dim0DsZyAZ7gfjPwASFklb6ffvrJeuV6GCBLDJMaUOoPGfvP5yQEEo5lS4ozKoIWuGZkZZmbx/BQsrSc+LjALGpE6Yrn4ukE33GVmX7MdmQjuZi/+OKLBJWDYE3y+5TaRBpk4Ck05+9nTZb58+dbrwQPFpunEJ3p3wixNxxjJtXcdddd5phwAxw0aJAMGTLEHGNuktz0AhkPVpIXFcEY6PmtVauWuRjJ+tKcj7WAGDIxxQkC8J988olxs4g9caFQuMtEZrc+Wop6ufiZnszcvEiETDGiwqJUFFjjdga7rAVLjwWriMHimnvetPiZ88BOhPH/9u3bm9eYYlOmTBnzHOeLWoUpAxXBGCZOnGiED7eH1dbIECd0MjTtW8SduEDsBxnm/v37m4nTvmA6DNuROY10li1bdtWqJjwQyLWafYEVioXP+9GeSHYecUQY8QLICmPtkxAjWWbHLbmxUchOQTtjvbp06aIDHMIcFcEY7IsBlzehIJjt2rUzXQrso2TJksaCJHtMVpnncuXKZd6Dbe0lLLH8cLURzkBOnwlnqCmk/5fvjO/zww8/tF4JDiRpuAFRBoVFTvE77q89wRsLkfgvN0dvoVuwYMHVuDDus78bnRL6RLwI2qOwcG/iG8sjmUE8kHKPNGnSmAsBa4KR855DVRG3uXPnmrFPBNhx+fg/QsjFTuAdYVSuQZkSE2EYI2ZPr0YcgwldJiRCOI7Dhw+3no2Fz4LVR3mNNxxrWwgJaVBSo6164UfEiyCuDSdxfEZWYQ2QHSaexO+Q0cXdpcTFKVA+cOBAk13md5h4wvQZxJPpzDr1xDdbt2413R58Z4QV+M6CBcePcp2KFSteF4+kPIrPwGgzXzBEA0uSmxwdKpROJdVCVEpgiGgRpCyDLg36gJ06GFg/BEsxKirKXBCMvJ80aZLpG/Y3PAGLAMsAVwkrg6QJ8SbcLi4UZuAlxYSVcAaLm0QJ3x+Ze/4f6JpCssEcE6xyMsfelhzHGAueY+YLEiksAvXuu++aLDLnB+4zLZU6/j88iGgRxKXlBKZg1xuKlimLoEOEOBGZy7Zt25rpJE69qJz4ZIYRP34HV3vChAnyzDPPmNgg/2I54OYp7vB9rlixwtx4cI/r1KljkhqBgk4dhIsV/XgP744dRBKLlBZKkife4C5T+E08GYEmg4wIYumH4rIIyvVErAgiZCQx6NW1Y04MTyDLi4uD1YcLiwVHCQfxH8ph/EE2EWuAGBEXBYJHcoQyGCwa3GASIffdd5+5oLT7IGFQvI5LavdyI1aJtbQohkesaOGjeJrwBmLoPcKMUWC8r69lRjl3OJ4kvmwrFSFke5YIVUKfiBVBBIoYDosjUQ6Dy0uhNK4P4sdAUCaecPE5zQskw0jRLWuBUCPIBco+Pa1F3Cwa+Yk54XaphXBjkLjC8uI75kZDcuno0aPWqwmDriAsP1xtBsEC3T/ZsmW7rnURUcNaxPX1BSU0ZJbtG5udMGPReiX0iUgR5MLhRMXKo7yFEU9YAdmzZzfuEYFttzpBLhS6Q2zxw/LDYkQ0PS0U9kN7GBctD8+aM+XG2LVrl6kpJNxA2IHYakKsQuJ+JLhuueWWOGPLSJJxLBctWmQ9Ewu9x9zE6O329T5MAifei5tOWQ8F9+xfM8XhQUSKIEkN7uzEA4n34RJz8pLhdZvmzDZYiLaw4eIyB5DEiq8LBLeNBny2IwOZFK1hkQBlRi+99JIRJyx34q7x7TTBcsdSo6wJi9CGjDTHihujJxxzYpGEOnwNhh0wYIDxKugcolSGY60j/sOHiBRB3Bs704tlxp2fuJ0TiBwFsnaAHiuSk99fVhkxxeKjzQqLg8Z9LAklsFDeUqRIEfP9MgwXK9EJXNZSpUqZ2j+7KNoGqx0BQ8i8rXWsfKw94oje4PbiRRBKQVwJrSjhQ8TGBO0ECNlbLgi6O7DSvDO/FDxzktujmGi8JzaE2+sP3OnBgwfL5MmTjZvNxUMcK5BZTeUaWHMMYkCAaGVjJJqvkAM1mZ06dTI3P0TLu8uD5BavMyTBu23PHnSB1e8N+7WLpukbT8gADSX5iVgRtKF9jawjcUFOYmrGOOHpGyWm07hxY/M8ge/u3bs7ujknT568KnxcSFiLWIH8PkXVSnChB5zvnDAHVrr3DY2kCokpLEESIK1atbpuWVCGIuBes560J4w5IwbJMAXvsAc3Ss4PYoFaKB1+RLwI2iBuBMbtbhBKWqgjpPyBoQpuWUi6SZo1a2Z+l2QJE4mJN/IzZTFu7rYSGLDwyezzvT/++ONXpwDhBnODQ/xYxMpe3N7bGuQ4E2ekS8UTwh54C8SPvcWV2k/ej0lCCR28oSQ/KoJe2H3BdJFwYhMfIoNol1F4Y4/Swg0jVki9GBcMjff8Pg9fxdhK8OCYYHnbFjmJEArdsQJJioE9zRvh8mxdxJUl20v4wrs4mo4QSmqIKdtQPI9oMnnGc96kEj6oCPqBC4OMI+1yuLRkdhm7T7O9DVYHK6khdLTf2VNPyCAylJPnqQ3U/uDkgSy+bdnzIMPruXASYseNy3t5U34PwfQepkAxPPux6zyJC1NwT1mNTpEJX1QEXSAuOGXKFNM6RYKDuBAz5LD+GLdPaQSxJabR2FAjhqtFjEgX6UlesOboArFvVLQ02qU0zA+kJIZElz3iDFjtD3HkBuYJCRfEkUlAwKp57Jf1SDx/XwkvVAQTAGOxEDju/LZ1gdvsPXafjDOvsa1b3aESfEhckChB8DguTO+xwxu0zJFV9pwCToKLuCKhEM9Zj8QVKXliLZrZs2cba584o+c2SvihIngD4BKTRCEjSCYRNwsLA8EjIULJDbGoSB2ZH6pQ54n7ihDSIkeslxFqxA6xBu2wBW2SDEQg/kffsCe06nFsqSfkdS1+D39UBBMBizPhEtmrkdGKR/0Z/yeepFZg6MEgDMIZHCNivQw5oPWO7hFPi55SF7Zh1L8nTKLmeR6UTHmX2Cjhh4pgAGDmHJOHKavh4iD2pG1ToQvxOyxAu2uI9scOHTrEGZRB0oPWSLpRPAcq2MkRiqPV0k8ZqAgGEC4kLhBGLmnzfOhDdt8uhif7j9VHTBcQxFGjRhmBnDZtmnnO7ihhe8RQSRmoCAYIinJJiDCB2HsUkxK6UBxNpwmxXcSNwnZ7sgytczxnD1RgahBJFIrinWZLKuGFimCAsK1AnSEXnjBMgeEYHEPKYOgBpqCaBZ+I9VIChQtM/NdtLWolvFARDACMy6KujFmEmgwJX5gSTUE8NZ6IIf3kJE2w8O3F+Vk3JiGzC5XQR0UwkRBkp0SG1ildOCn8YfoM9aC0zSF6DGMgi8y4fGKGOiEm5aEimEiIH3GRqIWQsmDsGaJHRxBiyOAFDXWkTFQEEwHtVUwbIVbkayUyJbyhBpA+YTLHtEtS+6lDElIeKoI3CLE/ekaxFHRKTMqGBAk3O3rBablzm16thBcqgjcI5ROMUyceqCUxKR/6g0l8UTfI4FZG6OvQhJSBiuANgJvEhGEuCO0djSwYl2a3Sfbp0+e6AatK+KEieAPY69AyUViJPFionZ5jzgHGbX377bfWK0o4oiKYQBizxBzBHDlymPVolciEUhmGZzCdOl26dKbFTocphCcqggnk/fffNxbAsGHDrGeUSIa5gnanCUsreE+pVkIfFcEEwGQYekvpIti3b5/1rBLpkC0maYIQMnmG1QqV8EFFMJ6QCXzppZdMSQxTYhTFEwrlmSzDtGlKaWi/I3SihD4qgvFk69atZqw+zfTBXDjp/OFfZPU338svx7UHORxh3WLKprAKq1evrmvMhAEqgvGAhXmYKkJ/cDAzgafWTpWhvTpLdJeO0qrTqzJvyxG5NuZTCRdOnT4tw1952QghS7EyjVoJXVQE4wEdAzTQs3Zt8PhVPu3dVp7u+7Z8v3GdfNi5urQZ+ZXs1bF1YcWf+9bJd0u/kfX7L8i8L+dJ4cIPmt5y1qGmzVIJPVQEXaAb5NFHHzVTRVhP2DcXZO+qz2V4j3bStFETadv9ZZn6w0HxdmjP7loi4wd0luaNG0vLZwfLR9/slKtFFSfnS+/WneXV6dvNj+dnPiM1npkga/epWxwunNs4WXq2bS/denSRjq27yCdbLsqOnTulU8eOV5MmDGZVQgsVQRcoiSEZMnToUOsZb87Kuo96SfmozJK7cDmpUbuqFI/KJFnyVZQhX+0Vu7Hq9JZPpUPJKMkWVUyq1K0l5Yvmkgy5ykmvj9eLGc60/3OJfrqLjJobO9798qJ+UuXp0bJ6ty7cHh78IV89V0ueGjZHNu3aIV+PaSl1us8wr5w9c8ZMGyKmTF3hwIEDdUH+EEJF0AH6RXPlymWWZ/Q3Tv3c2knSrFAayV6pn8zcfFCOHT8q+1aNkRq500jWKiNky5mYjS4dks/bPyAZspWWAQt2ye9Hj8jBDdOlR7nMcsdDHWXa7phtzs6XXm2jZcSMWEvw3KyuUjN6vFqCScDprV/K6J4tpGalilK9QTsZNHGR7PE+3FdOyqYvx8qzjapLxYpVpUHHoTJt7UG5aL0slzfJ8Nr15OVlsQtsHV8/WlpVHSgXL1yL6rI6IR0mLOLPMgx0nijJj4qgHyh56Nevn1mw278Lc1qWDaspd2UpI0MWH7Geg/Py49SRMnjUF7Lr/GX58+B0aRyVQQo0eVeuLdP9t2z8uJ3kTV9Q2n6A8P0mk7q0k26vzpJfT5+WJQPqS+vh82QXIqoEiSvyx7p3pPnDOSVjruJSq1kbaVG3pERlyS1lnn5Xttpm/JVTsvajaCmeJaPkK1VHWrdrJOXuzSIZC9SXN77dH7OXGC6tkkFVm8qoVfuFJbaObJ4g0RX6xIhg3AW3Tpw4Ydasxj3GKmRUly7KlbyoCPqB5RQ5ScuWLRtnKcY4XP5Z3mhSQHKW7idfbj8pO7/5TMaPHiPvzlwpu46clYuX/46RustyZPnzUjTjXVL5lbhtdse+HydVM6eTx/rNlmMxl9KZle9I1ya1pXat6lK10XMy7eej5oJSgsVBmdyuqNyRsZQM/mq7nDpzTs6c2C1zej8it2cuKr3mxdb5nd8+Wzo/mFayV+gnC/aflnPn/pCjK9+Q+gXSSlSjcfLzSWRwm4ysX08GL4lNfhxd85q0rDFELl68/tyZN2+eZM6c2SRMmFPYuXNnHcSQjKgI+gDRYzFuO5g9efJk3+7w0cUysHKU5C1dVxo2rCVF7s4jefPmkeyZMkrBKv1kzk7iPlfk4PS2ki9zHmk2KW528NzPn0jzPGnlwXbvSewKthflzOHdsmnjFtlz9KwKYLC5vFtmDe8mnYbMkt882n4PzGgtudLmlPrjic9ekq3ToyV/6ihp+pan+3pCZnQrKXfcVU3eWXss5udLsvTFetJsyEzZ8Ms2WTiqhdR7bl7MjTB2axsWdeeceuSRR4wYtmnTxizsxFrVixcv9n/DVYKGiqAPOBlpii9ZsqR5ENBu0qTJ9dOj930pz1fOKv+4+TbJX627fLxyX4xYHpY170fLQ5lTyd2N35PdZ/+SQ5+1lDyZ80qrT645w/DXps+kdYH0ck+LCbLRek5JSq7I3zGu6GXjz8bcgI4flv3bvpGxzQpLjgdqy5gfUbAjsvSVCpLhzrLy4qK4cyM3Tmgm+dMWkC5ztsmFmJ8v75kj/Z+qJ/Ua1JO6TfvK9F/iDlRg3eKuXbuaEIs9qh/Re+2114xlSBnWyJEjjcusJB0qgl4wHeThhx82a0r8/vvvpl2OaSFZs2Y1fcMs2H2VAwtkQIV0clPqJ+S1xbEB8VhOymfti8RcOBVl/JbD8tvsjlIgc5Q0/yCuy3N+wxR5Km8aub/NRNG2++Tl8qllMvypKvJgplvkpltySZ1hS8RI3uVfZU7PYpIuqoaMXRN3DZnfPn1GiqTNIU0/XBu7bQx/nz8hB/YekON/Xm/RrVy5UjJlyuRzBBudJo899phZ2Kl27dpxzzMlqKgIevHmm2+akpgxY8bEWThp6dKlkj17dnOismC34Y/lMqxGZvlHoQ4yY1vck37zmNqS+47C0vebfbJ/xQB56M5cUmtMXKk7sXqi1MqaVh7t/pl4SqiS9Fw8uECGdWgpDaqVkftzZ5eCFbvK5E2nY1Rtj8zs8oCkyVdHxq23NrY4MK2bPHR7Nqn/zpoY59gdkiDEmTmXfEFnEoMY8EJY12TatGk6vToJUBH04NChQ2ZqcOHChX02v0+ZMsXEb3r37h3jxiCQ+2RydHH5b8YqMm7NH7EbGa7I8v6PSZbbS8qIDcflj4OfSf2cGaVoxxmxNYEWu2f3knvT5ZBGY9ZcrSdUkpvLsnNWXymWLpXkf3KiHLx0QOb3Ky7pYyzB170swb2fRkvhNNmlyQfXLEF/EFNu3ry5Gbt17BgxRP8woAOvg5h0r169ZPduaqiUYKEi6EG3bt1MXIbJ0b7AVWZmHEK5fXvsYjs7v+gpRVOnkoc7T5ItJksYY+H9MlXaPBhzNy/5vKw8FWMhXvhV3m6YJ8alqiMTfj5utvn7+EoZ2TCfpM5TV8at9RRQJcn465Qc2LVVdh/+04oLWpzdJaMrZJA77m0nc0+flO9HV5FMmcvJ4K/jHqeNE5pL/tT5JHr2VtebGNnf0qVLm+EK8YHqBHt6NcJJ66YSHFQELZgSjQvCSXrmjP/iPDJ6rC0ybtxbsU+c3iRTepWXzGmzSLHaHaVv32ipeX8mSZezlPSeuVti+wIuyeHlr0m1fOklQ8HqEv38c9K++v1yR+pc0mD41+oKJxfHFsmLjctLtZ6z5JBnTfq5zTK0dAbJ8GAHWXzhUozF3l3uSRMlLd7ZZG0AZ2RWj0clfZbKMn61FR5xgFmUtF9SdRBfWAh+yJAhJh592223xZxz43TJzyCgIhgDsT8W2qaSf/16r8CPFwzQpIOkadOm12KGJ7fKvDd6SOOqj8XctUtL1SZd5fU5m2MuE0/+kp2Lxkn3JlWl9COPSNkqDaX3hAWyQ4uhk4+/NsiIqjnk5rT/kxdmb4s9XhcOy3cT20mBVOmkxLMzhBL487vnyjNF08qdJbvJPKuN8fcfxkitPKklZ72xsv6Ee1kLGd9atWpJ+fLljUeREBYtWiTlypUzViFVCuvWrbNeUQKBimAMdISkSpXKxPrcejoJXiOYnMzXbRvjXh05csLFNfpLThw+LCec30ZJIo6snCAti2eUVNkKS7WmdIyUkajb00nB2v1l7i7rIF05JRs/6SLFMqWRrEVrSau2TaRM7vSSPn8tef27g5a17wxdIfSfM3R19erV1rPxB3e6ozWIoWDBgmbJTyUwRLwI4vqWKVPGJEOc3GBPWrZsKZUqVbJ+UsKdi7+tkikj+0rHVs2lZYce8sqHi2SHj9r4/SunyCt9OspTzVtL10HjZMH2hM05w8sg5PLqq69azyQcwjF27SptnSTzlMQRtiLI+q/M9+PRqlUrk7Cg+t7fg+3Yhm09n69WrZpxg/Pnz2/Ezd6n5zaeD4ar5smTx8RpWrRo4bq9/fDczvszeD8Ssl183tt+xHd7ezu+r/h8r/yb3J+V/8f3M7Ddtb/raen0bHfp2rmtNG3YQBo2bS2du8X8/EyHOO/f9umO8mzXLtKpbVNpUL+htGgfLV26dJb27dw/q/06iQ6qCzh/fG3Hw2lfrHUdHR1tOk6wCHngkbi9N//yezt27LCuHsWTsBVBe4S5PvShj/g9mGKjXE/YiuCPP/4oRYoUMQe3Q4cOMmfOHJ+PBQsWSJ8+fcx2lLZgQfrabu7cuaaViaQH2xL3mzlzps9tp0+fbvZrTwO58847TbuTr21xX9iPffeuUqWKz+14f/ZJXBLLlIJZxrL72pZ9sqIZ/afss27duj63sx/z58+X0aNHm7gnTfv+PiufgQeuPvutWbOmzJo1y+e27JPiXzocyJazf1/bsb+FCxcai4V9Yg3NmDHD57Y8KE/i706dOrUpWu/Zs6fP7dgvCQN7v3wX/vbLPvl8tKaxLYsg+drO/vvt0pTixYv73M5+sN+33npLsmTJYrZnGVbP19kXn4nxWbz+xBNPxHnd88G+mDlof0YW9fK1HQ/2y7nauHFjsy0F/MQIPbexjzmWJws/kVn2Nw4u0glLEaR0YMCAAaYHk2CxU9kACyQhbHnz5jU9wU4MHz7c7PPJJ590HYW+bds2s/QmbVCTJk2ynvUNMSB7kSZKJfyxceNGKVWqlOkqcFvRjsW+2Y4WK7e4kJ2ZvPXWW82F5sQHH3xgWgbZ3mlZUYrJuagRKwbPOsH3g1Ag1v6nc8dCXBYrn/0yfNQpk8rqbuyXOjq+O38cP37cZFUpM3nhhRfM+eMPkmTMkCxatKg5xk4gKrjWfK8cY88OIxs+I6GTxx9/XPbu3Ws9ez0s3E6oBcF6+eWXXcdrccPErSaevXnzZuvZa/A3cxPjhvr2229bzyq+CDsRpI2oR48eV9dtcBJA+jG5oLm7LlmyxHrWNwSZ2ScXqpsAkt3jBORC5QL3d8LSHI9lRwE21pXTuCQWcLrnnnvMnfujjz6ynr0e/v5BgwYZKwlRZfCrEwx94ELBYsBq8XWh2tAqyPtXrlzZUaz37NljRILvCwF02idWJ+LDZ3XrfEB0KQW5+eabpX///kYY/IHocIHT581kFn/w99uWLd+bUxsaxxILvFChQq6LqHMsOVfYLxag9znAzyNGjDCjsrixOR17vmsEi32RQb50yXmQ7tSpU83NmpuwL/Hnb+Y92R83Pafjo4SZCHIC4x5x5yVITLmKP2hWx03l4SSAnCC4tdyBOamd7tZgC2CaNGnkvffe8yuA7JeWp/gIIN0AlD3grjpZgFgwL774ohFA9unWfkVNo6cA+hvTxGfFtbUF0MkC9BRArEanCwxrFQEkBMBncYL3xK1jvxwPJwsQ0eE7wAJ0EivEoEKFCubvx6p0EkCOJQLIcfBlWXmC5U24BLHGavMWLVsA+dvJ5LoJIFY3YQX+LjcBJAxC+IFQkK8hC57HXAUwfoSNCHICIyqc/MQAneIbngLor1kdOFmxABHV+AgggWUEkIvFSQA5kRFrhBVRcRNAMtNYlViA/k5au3uAz4obenWIgx+wuhAVRNjJAuR5LEAuWIQ1vhYgsdX47vO6EWRe8J72Z0UA/dVqIuJYSnwHiIubAPI98VndXGCsWSyrfPnyObrVgAASLuHYcjx8CSCjsThP6RBxOva8hgDyd8dHABmowI3ygQce8FkwbQsg+5swYYLf46PEJSxEELcIF9gWQCc3CQEkTuTmAjPbDQGMrwX4ww8/SFRUlLlYiPP4s6psa5WLDwvITQBJ1nBnd3KB+axYHJzcuItuLjACyHa4i07WAH8DFiCiQvDeSQC5wBBAjgEWoD/sfbIdVtj27bFrpviD7wcB5DhwPPhbfYFADB482GzHhU6s1x8IIDE4tkUA/YkLn5W/hZtafASQ771Ro0bmbyNx4X0T5H0QQL53rFSn79O2ANmXL3faG5Jx7JfBCpyL3nB8mIJuxwBVAONPyIsggte9e3dzQuMCOwngqlWrjPjxcLIAESosDkSFTKBbsN62AEluIID+wIVDrHGTiIG5CSDJGi5AJlf7A1Eg/sXfz0nOjEMnuBgQQGJRTkkQW6wQazcBRFTIbmOFOIm1vU++V0SIIQBOeAogx8OfEGDFITp8r/xtTgkLauHYBmFHAPlMvuB5rFm+f46D26JHR44cMa2SiJav/XKciH/yupsFiOtPQgvB4ubmJlgkazhOxIx9lblwzPkeCWdoEiThhLQI2hYgJ0C7du1cBRALkGytUxYYASToTgyGLKSbBUgpDgKIBThx4kTr2evBPUes2S8WoJOoLF++/KpV6WYBcmEhKkwgOXjwoPWKb7gYEB8uBkoi/MEFPHbsWBM3wmV0swAJwBMDRTT8wYVMaQv75IJ0SyzgViJW/G1YgP7Eyo6D2p/VSVgRa94bAeR3/MF78b0jgBxbhmc4QeyVzC37pSrBW7Q4TpSjIICU6rhZgLYA+l/G9RqzZ8823xEhE7wcb2wB5AaFC6wknJAVQQSP0Vac/GSB3QSQLDAiGB8BZJ8IoJsFyMVhW4BOAkiCBgFkv1iATokFssAIIPt0E0DialwAWBZOFxbYAsjFgBj5AwGwxYrtnT4rokKtHGLtJIBg7xNr1SlbC4g59X38bX379vXrrnK8bAEktujU8ZAQAST5RAgid+7cPl1LTygvogyGz4q16i2AfEaOE+9LptqpsgDrkNALYhkfAaTeDysZV50bpzeEPTiGxJPdSp8U/4SkCJ46dcqswMXJjwXolCnErUQAaUx3igFiUXASs08EkCC/EwSebXfVyQUmTsQ0YPZbvXp1vxcBF/rXX39tatAQQKcsMAKIqGABY1m4lexwMWAlYQE6CSDfATErPisi5CSs9oJAfFY3AWQaN/ukLMMtrsbfwoXL3+YkgNS5UdTMfrGsnQQQqxNLGcEgbugPWwA5pgig2yADaiFpOcO6jx2kG9dapaaRLDB/S4kSJRy9Cr5rBJDPSELFDQriEVbOQW6c3hBrRfQRQLUAE0dIiiCN5mR26Xt0sgCBab0FChQwXQn+4ILigouvAOJ22AkLJwsQuEMTq6EH2Ums+Dvo38yRI4djDJC6RywLLiwsCzdrFQEgAUEMEDFygu+BEhAE0MkCBEpKEAqy4P7gb8IN5HslW+u2LgbJDN6b2B7HA7H3B1Y4SQCy61h5TvB3cyN0sgARLDsLjCXuy7X0BGuVXnL+NhJdvsSa75AECALodE5hpeMC83c7iTRgadJhhLvM979s2TLrlbhg+XEuuR1zxZ2QtQSpiHeqA7QhUOwW1MZF5mQmG+cmgJyEWB5YC/EJMlPOgYXnJlZAPMutawUhwaqlDsytuJjPipjgXhHjcwPR4bM6Be1tqJVbsWKFo1BxcSO+iLXbHEawy4awqpz2C1j/3GDckiuANY7l5ASWE6UlCAt/lxvcqDhnCMk4fVba09xuKLa1SHLHDd6LYm08Bo6VP7CMEUhv61RJOCGdGAkUXKxkLd0sCkBYKEhlPZHkgCwkn9WpBMQT+medrLVggruIJeIWV7MhXIEFkxw9rNxYuak5VQ14smHDBnMc3OZLxgdE1ylR5QmixvF0u1kqgSMiRFBRFMUfKoKKokQ0KoKKokQ0KoKKokQ0KoKKokQ0KoKKokQ0KoKKokQ0KoKKokQ0KoKKokQ0KoKKokQwIv8PejPhKIgF+WAAAAAASUVORK5CYII=)
physics-General
physics-
The centre of mass coordinates of a block of shape shown in fig. is
![](data:image/png;base64,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)
The centre of mass coordinates of a block of shape shown in fig. is
![](data:image/png;base64,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)
physics-General
physics-
Seven homogeneous blocks each of length L are arranged as shown in th figure. Each block is displaced with respect to the one in contact by L/10. The x-coordinate of the centre of mass of the system relative to the origin O is
![](data:image/png;base64,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)
Seven homogeneous blocks each of length L are arranged as shown in th figure. Each block is displaced with respect to the one in contact by L/10. The x-coordinate of the centre of mass of the system relative to the origin O is
![](data:image/png;base64,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)
physics-General
physics-
A rod consists of two parts made up of a homogeneous material with square type cross - section as shown. The position of C.M from the end ' O ' is
![](data:image/png;base64,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)
A rod consists of two parts made up of a homogeneous material with square type cross - section as shown. The position of C.M from the end ' O ' is
![](data:image/png;base64,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)
physics-General