Question
A geostationary satellite is orbiting the earth at a height of 5R above that of surface of the earth. R being the radius of the earth. The time period of another satellite in hours at a height of 2R from the surface of earth is hr.
- 5
- 10
- 6
![square root of 2](data:image/png;base64,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)
- 6/
![square root of 2](data:image/png;base64,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)
The correct answer is: 6![square root of 2](data:image/png;base64,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)
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Neglect mass of the rope:
![](data:image/png;base64,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)
A mass of 6 kg is suspended by a rope of lengih 2 m form the ceiling . A force of 50 N in the horizonlal direction is applied at the mid Point P of the rope as shown in figure. what is the angle the rope makes. with the vertical in equilibrium ?
Neglect mass of the rope:
![](data:image/png;base64,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)
Two bodies A and B cach of mass
are fixed together by a massless spring
force
acts on the mass B as shown in figure. At the instant shown, a body A has an accelcration a. what is the acceleration of B?
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)
Two bodies A and B cach of mass
are fixed together by a massless spring
force
acts on the mass B as shown in figure. At the instant shown, a body A has an accelcration a. what is the acceleration of B?
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hpKI2BQGBpgCrI1glVUx4VkRSTY9ii8qICtst38hmRTTaKcxskMQBBGgOBQCAQCAQCdRGkMRAIBAKBQCBQF0EaA4FAIBAIBAJ1EaQxEAgEAoFAIFAXQRoDgUAgEAgEAnURpDEQCAQCgUAgUBdBGgOBQCAQ6EGwvI3lbuoVy+iU/3sVainV21R/r1hHtrpU/1a7T+3v1d+39Vt7xT7lNYXV/2+v2E6dLPsT7+zvfgRpDAQCgUCghwBRskastWJnzJiRX9U3ffr0XMr/fVrvtaz76u+pU6fmMm3atEXb+7/vLNY9ZcqUvLD3HXfckW6//fa8iLdP3/nNq01tr/h/2d6n/RVvuSrfl986Upzv5ptvXlS8prAUC4xXF2/pUiw4rh1eeOGFTDwD3YsgjYFAIBAI9ABQ1R577LH8Kr+jjz46DR8+PA0ZMiS/6u+ggw5Kw4YNy8XbpUaMGJHfke/T37bzesBS7DN48OD8vuh999037b333vnVgYrXpXqFoE/fK7azvTJo0KD898CBA/OnV58q5VidLd7rv+uuuy4q/fv3T7vsskvaeeed00477ZR23HHHRcXfft9nn33yaw4RSwuSB7oXQRoDTQdhitoQSine4OI1V9504M0H3oBQQhxdKR09RgmtKAsXLswv9VcfdfP/Ui+/+e7NN9/Mv9cWv3kzg2I/11d9bPt5PZjrDS88EGheCL16panXlyJrG2+8cVp//fXTWmutld9f36dPn7TZZpvl4rfqstFGG6UNN9wwbbDBBmm99dZL66yzTt5vjTXWSKuttlpaddVVF5VVVlllUfG335XVV189rbnmmvlcyrrrrpuLYym+c8zqYvuOFOco51555ZXTX/7yl7TSSiulFVdcMb+b/09/+lNabrnl8qe/V1hhhbzttttum84444z00ksvtbRWoLsQpDHQdPDKP+GLK6+8MhvY8lL9iRMnpgsvvDCdc845+cX6Xr5/7rnnZq/9oosuyi/at92ll16aX8Z/+eWXf6r4zm+2KcWL++2n+H/1b7WlHNf/1cV5S/HCf3U577zz8v8VdfWpvmeddVYu6lxb/K7Y1z6Orbgmx5wwYUI+jjAVMh0IBJoPXtfn1aOnnHJK2nTTTTPh87nddtulAQMGZCJJPaQCUgapdpTCUiiHtqPgUe/69ev3KdXO36VQ9hTbFaWv/N/+juN4pey22275u9pSrRo2UoqyWH3OUhd1rC7bb799JsqIZd++fdOYMWNyiDrQvQjSGGgqUPGuvvrqbMi22GKLtMMOO2TjxRAyrv72uc0226Stt946bbXVVrn4v+8ZUAaK8ao1er4rBkwpxk0p2zOe1aXasDLcDLn/274YaPuXc9QaW7/ZphjKsk9rpdSj+jj+dl2u8fjjj09PP/10To4PBALNBREU778/4ogjslqIKI0cOTI7rEKzchHlBfqUD1id93f99dcvKtddd12aPHlyLtdee20uvqveRin71paSU9hevmFXSmvnqi7lfNdcc00aNWpUtuXs22mnnZZefPHFltYKdBeCNAaaCsKwp556ag6r/Pa3v81hGV43woZE+b8cmJK3U4hZIYqIHmJnOzk2tvV/xT5+8+n76nweeT7yhOQNVRd5RqUcfPDBufh/yS/y/6FDh+Y8pEMPPTTnHylylfxd8pNsU11811Ypv9uX8sAjF/Zx/QYTIe1AINBcMGN65syZ2T4IMwvJiiwIydampfhbaktHin2aqbBjJs6wv5x9EZUIT3c/gjQGmgrz58/Pipo8GDkyksXNAjTD7pZbbsleeJkh6HvfVc/S87dty8xBn6X4vvq3cizevZmDZhQ2UsxWLJ9lJqPZjffdd18yC1Dxf8X3HSllVmQ5JjXh8MMPz3lNSCNFQS5kIBBoLghPmzUtDEtd48iyV705cvD4449nJxlplKoj5zPQvQjSGGgqmPhx8skn5/CNMDBS15sxb968rEZQVOU6IbwmzQQ6D4N3mWDl06C9JNaHoyxRVExwqp7sRBVanLmprsHEqzLhygxUir3i/5wMv8caeN0L7S9nj6ImMiJawWHVR3orpNuI1kg7krdt0l+gexGkMdBUMLCOHTs2h6WFjiluvRkLFizIE28QaGEcykSEpzsPZO25557La+TpW9Tg2bNn51yqxUnkEDUqCgWbAk4hLnln1G7r7y0OxVj/MEHKOUwcM+FLf+FomFhlMpXJW35/9tlnW/YKdAc4K5bbEUmhNEo94RRzInor5s6dm5VGOd366muvvdbyS6C7EKQx0FSQz2OWsYktjKoQcG8Gz9usbTmYcqGEvilkzQ4KmJmkyJtQv3QBxEbyvHQDCgxC98gjj+SQnm0V4SsKXiOgrtne/nPmzMnkyvHNXpWPWiY4+b/vpAI456OPPpr3a7Sd1Qd5MwA+/PDDmQhQTY488sjs+DhHmdREYfJ/A6V+LkXC5AjXZtUAhBaBldvlkzJVyquvvprPQ31GSKVGmHUvH1feq8kEFBuhPpPILNGyySabpC233DJPwjr22GPz5ANtq92dTxs1Amqm1JFyjQi3e4YEl9UNkFPEuBwfQUJUtSWFtSOg/lLgEHlky70o53dcbaYOFqNGzP1fvmA5p/7VaD9ZWigTYY466qh8f9w39783k0b93vMXSmPPQZDGQFOBoedxGuSELXo7aTTgIo1C02YaGhQNPs0EYTmkA3GgrhnUEQ6ExzXJ2TTxxzWaqKQYUM0slf9l/bZx48blCVLICSJJka5O/vd/BKiEghEuZNQySmZljh49Oh9PHpl18Kwh95vf/Cb94he/yGvGmckqBQCZkx6BACE+SJpjOrbiPKX4WzgYiTKDVdgRMUMUETXr3llWxWdZW8+adNams24eQqc+8nZdp3pqEyqhYiknaqHie9dy1VVX5U8kV3hz8803z+vd/epXv0p//OMf83Gtr+e7X//61+kPf/hD/t6kMr+ZfOGcJmmpL8KFoJbQeWm/Uqja+qC2KNdoIWYTwjgyiDAHz7WoC1KMBGiH8ePH52ugfjoPQuz+157HOZTyf/du1qxZ+f5xkgrhR0i1hX6g37hXJrNR4NkKC2FT8ZzXCgwUZPevpyxTVUjjMccck++D+rvG3hye9uy4f/qQZdT0tUD3IkhjoKnAsFqjULjCQMCo9mZQmAy8BmhLdRg8m01ppBCpN9JheREJ7yeddFImi2aZU+QQEQqMe252O3UOeTSgKGbFmyWPWCJYiDQSUdRJCprvOBwUCyQTSTSD3r4IoYLUUDWEB6k9JhhZK68s3USxc26EDDFRV3V2bIoaMuJcyJvvrKOp7sgLRwcZUAyCPp1PHcpse9dECfS7OjifJZX8raibffR/x/N3+d1nWd7J775Dds3EdQ2OWxRNvyHH6mA/pM620j5cs98cA1lHQJGxslZpWYNUO/peW7pH2t65nUdxnqLWlvb1f6TZ9SJFZRUAJBL5d3+cw7mcQ/uVtUqdS0GeEWn7uofuQ3Eu9A/Hr27Hco1l6RbkVV3U2fmkAnBauhscYuRbvdxXJHdZiRx0Fu6NfuXeBWnsGQjSGGgqUAUMVgZTg2xvJ43CcYyp5YUMvsJxVJpmgIFaaBjRMugb8BGJE088MStpcvCEN4Vzy0xzCiRyWQggMkH5c+1l2SQkUuoCooZMIypIg7drUPWQI6SI2odkITCUxkIAKV+F/CGC/kZkEBiE1KBOSXMugztyiYgUgoKYOL7zFPWQioe42QeJrL2+8s5f4Ujf+Y2aefrpp+frcUyrBVAHf/7zn2dl8Je//GX62c9+lovvlN/97nd5O4TJdTkX9c/xyhp4yLS/lbKen2tExhAVgzTCh0ha2spKBdpNezmuAdy1aU8k07W6dvu4B+4hokn1da/Kenyuy7kKqdamRZmkbLpnCLx75ZjIrvO6Huqov7VzIc7uHcKNOOozyKtrcI/0J/eJauf4CKV2ZDccxzGF5xHvE044IYevuzsXGGnUz12PfuReNKMTuDghpaCEp2P2dM9AkMZAUwHRQBQMUkKUvZ00yjuj0CBGchoRD6HRng4DpNAT0mAwRwIoRAZ8xKmsTed+cxRsr8hl852BFDmWGC9/zz5Ilr6BACIvSI1QL4L1/e9/P33pS1/K5Qc/+EH+HgGhZCIw8hSFRh23nNOnOsij9b12VS/kFWk1uFPlhH6/973v5eP++Mc/Tj/84Q/T//zP/6Svf/3rufzv//5vJo7IGJXOdat7OY9rqr6+cm7F+ZA8xAeR+uY3v5n+/d//PX37299OX/3qV/P1fOUrX8nncI0//elPM1FFwlyXc8lxdA2OXX18n6X4mwPC6UCYTTZDqBzvi1/8YvrWt76VSeryyy+fianzfeMb30g/+clPMqk0qKsjIuhePP/88/mcrZ1H0Z5ImpA0woZgUsoRU6+R047OoR2/853v5PP7229IOoLJWUDyrRhAkZL/Zrate4lseRaQDiFfaSzIqv7mPBRXbxtBHp0TQRMid7+7axa5+6/e+hUngZLqGrRjb4X+ywlhHzzb+nKgexGkMdBUMPBQfKgdQRr/SRqpUQZBA5/wVk9XJgyCBnm5Z8guB0A4Ua6Z+puk0BEYbOW7IZDy3ahbCBp1D4FDOBAs5EdBuH7/+9/n81LEkApEplEgj4iJQQyxov4hh1/+8pfTd7/73fw39Q+p+q//+q9MrJAAKpicU/XtCJBZk38MnI73mc98Jn+6ls997nP5vEjrj370o3xeZJnyJrcTSWwUyJJ2RB4RTn0KEXUexy+qJnL8n//5n+nzn/98bks5nxRU+8hHdYyOQH+Vl8hhQOSRU+3o3HJK5Zb6+7//+79z/iUlkjpIlUMiCtmXumJSjGsueay+d2/ll8pfRGbtx4ZwVqiO1FTnpU4KB3eX06X+cjWlYbBvlOJYcufpTKKpyqE09gwEaQw0FQy4wtMGjghP/4s0ytFiXHs6aTSAI04IAtJm0DYgUEsRB05BV4BAFMJjkgd1imqFJHqHbVEeKVaIHFXSQN1RIFaIh5As0lRUxnXXXTdfDzUM4aEMOrf0Af22M8vaaBPqHYL6ta99Lf3bv/1bJlFUQASL0uncVDnEkXpGQRXK7yiBgyeeeCLP3EZcXJdjChO7V948hLg5F+KIkCN12kG429qPHQVCRwlUZxODtJtzIL/yKh2beoqMm8Cj3yDgSGBnwGmRFiEkT7E0CYmDIXQtZ1KObXcAaeSMIPzSANSNiqp9eiso0eya9mAjOIWB7kWQxkBTAWmUIM/A88SDNP5LaTToCvX1VGWCkkXpEVJUX2FNA7bcM2HEjqhirQFhkTtHcUVwkCpEQwhZbqO8NrmIVKVybt/Ls+uIukTNKiRHbh9SiDjKWXQtCJdcOqSHWoakcnJ8J6fQwNfotSKMiIR8PTl41DbhWuQNoeI4UfnM9qZsInHCx0irdAUh146oqEg3MiW8j0ghoyuuuGJWgrWra5Z36PwUVNfnU3sj4ByCjkBfpaZpNzmU8jIRYaF4ZIG6pCBQCKW29inErO93FuxIIf7yBzkTiKkJWN2lZulXyCxCjCi7Zv2lWXKUlwQ4WcL0HDyRCfajGcDWuZ+tFc5Be6Vs11MRpDHQVAjS+GkYZBAKSiPjKietpyoTDCJSi8yYQIFoUc8MjF2ts8EE+UMM9Q0EQDH4Gmy0CyVTPqLcO78hV4ijmbjqhTA1AuFzOXjUD+QT4aDKmQGMACEjlnMx+CNCSBeiI3fOPZL3R91sRAXULpRT95f6RoVD5oTf5VVSlrWfvC/KKiUSqaSkIsuIqjy5Rogj5Y6iqY7OIRSN8Lo2YXzPmlC+CS2Oq50pkM4rZ1O6iPZtFBQ/4WDHQr5dn/O5J+pgoXpKE+IgX1XeJFVVG2h7k4k6o9wWaBNOBgeGgkmJFhq2IkF3ANFwvUiytA3taRJRZ9TiZQWeJRPkOGRyWJuFNOpbUiekiHhGS5EaweHkzPn0N4e55OB6xhR/d1ZJX9II0hhoKgRp/DRMAmFMDaJUNMaou3Ky6sG9Q4AoZGbDCqNSr7oyEDgm44owGlwQMxMcDLrIokkk1XmEFD4DMbKKgAitUpoQbwN2PQj9M+jIBSURWUKq5NghjNXh2bIcEmWOEkglQ8YQQOH5stRLaxMvfEeFQz6RWsoeBQ7ZRRBdV5kUYEKJAcj3iDDiKJcTCUK0XBvnol7oHyF0LmSTSlvC0lTA6n5F+bIt0oqkUwXVT5si09qgtHdr4DyocyHwzocwIuAUJSqi+2mx8gLkQRsjwyb+IKrInsktSFVrbVgP9nHPzLKX14jcm0DUFSLaFaiPZ4H6KZ2B0ojU9nbSWKIDnplmIY0cInbHxDe5suyFwrG0VihF23NpYhYnQeidHedAUfM9c5yzes9SdyBIY6Cp4AGSG2agZ1R7O2kUumSU5HkhDY2qSt0BhpSBlPdnFi5yx3B2JYeMUbVkjTYwsBj8tYVJKgYYSl1tKBgRY5wRV+FQxE/b+b4evJFC3ptws/2EgREfpMpC3tXkxf9NzjFwcHIQHeFeqpZJLfqxRP/WyBxiZeYo4utcVFkkUCi6qE/VISxtS6kQVqbEyeVEUhFbEz6EnOsNuAYp50KkhZ0RtGpiVg11RuqogdpOeBrBdC7HaW8yk3tC0UQO9QFkWF090+4jImf/6uvz3CPGFMnPfvazOVeU02EAdt9cf0fh/lA6DdLaCWnleJiF3R1wvQir9AZOD7LklZI9NXKwNKA9EHl9g3LfLDmN7iWnkR3yTHKGOLScAYTQpD/Pv2Iby6Z51jlh7j1nzzJiJsA1GgFZWgjSGGgqIETVs6cN1r0ZQq7UIYTJ4IdEIhw9DQZ9RpRaJJxLxRKGRCKr1bmOghLBQ0feKEXCwUKpbeW7IQoICSXLhBVkhTpnUELuLHHTnmevvbUz5dB1yPVDkhDGtkANRm4QK9dtcon9ERSTVdoiBVQm4XXbItmIp/zVtsgfZbLsI7RssgxChmjJD6TstZYrhVRrR4OZHFAzzdVTn6KI6FNtAeEXOlY3ZNU9kNvY3tIo2orCIkfTeczMFr5XR4SxrUHSvaEKmrFNbURuDbDO35l3EmsLaQIcCGonJ8A9ae96lyQ8twgrcoSsS+PgFC+OHGX9nrqr77dmHzgFnk/n118p05yCaieoGuVNR9I6ytJGJlAt7rUu1Uk0QnQCsdIHmgWUeQ6t+8guef7lUCOKwtL6mfA11V4/FL7mTCGU1h+1rRSMnva+7SCNgaaCAZbxoCbJ65KrtjRhoDHIKm0Z1GrYTkhTqVW8FgcYboM9L1b4o7tCa/VQwroGAEobQkOZ4mV3ljQa/AxYjCtSRSmizhjA6kG7UTCQFWFqhKEscdKaauVeIzMW+0YwqXAGAW2OSLYHAzLFAMG0H5JE4eT4mBRUq8rpYwZfbUOJE7rVVtrO9banPBnM7Wd7k2aEqhFjymZboVznMvMZSSzLBFE2tQelq979MeBx4EyIQQJFAAyErSmozo3QU1EQ2rL8EZIk17O9ARJB5XQgpq5NH+J4+K4zk2K0s3pSil27NtMnGlGclwT0ZyQCUUf8Pdeemc6shuDa9GP9AYGXCsGhcD85CH5T9Ad/c144485N7RUK1tdrlXAEFnHTn83y1l6eOYTf2p5Ij+fE+bsKx0BiOWn6LwdzSU5SIkh4FrSZZ6yrYWF9XX21q/QhfYyS6BluK4XINbsf0ng8x+05Ud2FII2BpoKHmtqCJFkMemmSRoaE58tDNNjUM2AMMnJCLRBas9/izjd0fEqjsCKFp6fm/Lhu90ooE7lD1Kg7DGpnSCODjGAIFUuSF7rlSAh3N9IG8hcNcvLx1MUEDDl5FrZubbaqgVMoEzkSZkZ8hWINrNW5d61BXakwFC2heSFqhEd4XH1r99fPKDiIFTKLELs2bYUA1JK+WlA3CpFGyhA5aqPnBgmodV6QAEooRdNSOlRKbapuBrB6yjVHBXGzf5mk4r5Qq2r3RYBM3FEf5FQYnOKIrCBr7Q3UBk/Ki3tmP4oowom0IFsdhQHaOdWdI6BOBnXP9uIgPR2FtioklrLGISl5rx2FfSiGcl8pl9qI06JPUdSpzggp8scJ55BQbdlV98NENaFUqhcbo//rl/bxJibbC7vKz+X8UNL0UROYrJO6OJYtcg0IlmfOs7mkSSO7ob0oga5B+3XV0ecQcoaQXm3rOdNX2+tfnm/7edYR2CUhNnQFQRoDTQWTHgz2vDaDdlfC0x5cD6VBD6FjoBlF/zdAeXgZSgOncAJDIt8IOaMCGBipTNXKlEHR8ahd5a0hjKulURhgHj1jhCh0RkGoBQNEGWBUGaRGJnN0BxBoa84ZAKhtlDYDDQNdq7Q1AuTCgC+ciMTJZaR6GATd03pAOKlr7g0lD1FCYpGS1kJsFBbev20QFiSV0mJAbeQ+ut9IXwnjUgDVGzGoVclsq2/p47YVBjeA63/6Yz2UXCqDOIKqvvL/OBfIQnW4U92RYaq9ML0JNAgx5c+klkbujWeyhKi1pck6jqev15JA7e45sJ1Fw4WYDajatp6iot6ULMdGFsvC6ULWnVlr0/PvWUSq1MG9RRo9//WI+ZIA0ihEqQ6cQJ/+7gxpRPI4CGwQ5de1cdaoqUKflETXLbWjvIKRU8GxQfo5ABwW95S99ewqCJC+pS8jj2Wihxw89x3xRkw5iJ6jrpBv18ABUl/1cN4lGapl56VNeNZMXtMuHBxE3m+dUfw4xGyK9kEaHdMEmbaIoOdxcYwLSxJBGgNNhaKKMIKUxq6QRkYJ6TPgMZ5UMAaW6kEdNPgy2gwjY4r48cYNxrxxhp1KgWyWcI8BR8jRLDnGR3hROI2qhNg5BoMtTLQ4DKBBT33l5zHeXVm7bkmCwTWBo0zUsCyMNtRWjZC8WjCsBhQqBzUNsZJIjrA3MlBRE91jAzMCSPkzUBogqRm1pAFhMZnEoCgn0T4G2vZy96rhGqkYCI68Qa8CROj0OYSnWpFzDe4l8iYMa7DXL006aYQ0un5OjsEWOXdtZm1Th1xz9THUS9haX1af733ve7m/qqe8z0YGSm1TZiEjwgid+6K9qgkqGDARZeFvk1l8UsA8D/XCgdrI4I3cICiIN0Jsf2S4o0TP9pwsjguSLN1A/plzdAdcv+vg/Jg44dN97AyJcG3sG3vE0TWBqij8+rDUAzYN+XPvtIPz6M/sHVuFNHLGqLCUSrnClHiOkn6DzCrO4TdkU7qAT88Gh7arKpn2YDMQrpLPqx+0dq99p+/7bO13KL+VbR1L8X/PPYLnWfDs6WPIHsfU9XCCTMTRp11XI3ZGO1lBwTHlXRMckNDW2kU9qPPGpJ68NmeQxkDTwIOOFFH5SlJxV8LTDB6jzOM24JlByVAYhBgJXnVRFpELRX4NIyZEZlsGFXFEiAzqSBBSy+AzNtRQoaaSCO0cCB6PdnEQPGFPBluYCNFgdNoymN0JHjc1yeCMyJjdqw2Fd1tT9upBuBupQTxNijAgMs6NkCpg+KnK7q3BEQFB5hArJK52oOYQqKuwHWLlfPpNo8RfvRA2pASp8lYXhEcfMTBWq0kcAWE+9REuLvmMBvdG0xsQT32wHANppDRSFauVcW2vn+uXCKpQNlXSvgZJCnE9aEvPob4uzE+1RUyEE2vD6Z4314yYIrMUR86VczUyCLsvcvP0HUojh0HfRzprCWojQBQoqp55hMd1dydpLGkJSJLPzpLGAve6hODdV44BB9Z1uu8ISomqFOj/ngtKt76qr7N5nGv9qrr/gD7p/unbnGR2DsnUJzqjklZDe8jv1D85G54h90y/RbzUGzlGstgYz6NP/dYzp276hU/b+N6+yBxFHwlFBO2H/LLL5W1OngVLT3Fs9Df3A8nW/xA/50H02oNzIeHIp+N6jgkdte3iOtQDKXdf2ADX1RMRpDHQNDCoIElCvgw8Q2Yg7SwYaQMEpYWRM7AyELx8nrhBFiFDBIU9GUEFWUHQqCkMMGMg7CoXiafqd6qScI7thTioYEJgPHcGEAHlsXcVEsWpY8iYOmmfRgbfpQ1G2eCMMJsAIQzK+9ZWnfGq7WMQ0w+8BcW9c58aNbQGFGTN4OieyI8zUFCC3bdahc1AqZ8YPCiNiKYBptEFeO2PsBn45Bp+6UtfyuTZQEuprq43hUY9ED4DF6KqnupbO2C3BQOQcwk5I+gm/HBmDHbV5yqDGkJhEgzC53zCaFIsGjmfYxhIqfCuSZ2ReWFoIdLq/kgdpnppA+QbabRfI0pjgTw3zpp75t5TxTgk8ug66jDZx75UWX0Joe2uJXcWp9JYDURJuoN8Wn1clEYeo+usVbzcK8+qFQE40mWCGcKk77QG9UYmPQ9l0X5Ej91rtL+2BveSfXevKfvuEUdEX9EHkGFED8n1t76FvLK52k3/9ZvtfIoaeQa1MfLpOOyPeiJyrtkzo504dGWWvuIZ0lc5Q8YdNleeej0nVduXFwFoG9dA2VY37e/5IB7423OonY0jHNogjYFAF8GIeMA82B7eroanHY/R9PAKT1MOKSWMqsHDoEdBdE7Gj3eoGCQZHCFD+yAQQtZIJmNVvFvG3oPvk3Ez8COMjHBRSet5qvVQTRqFxJ2n0cF3acL6hnKgCmlEGJBGZKNR9awa7gGCToWjpCFFlMZGj2V/7U+1dv8MEAhWmTHcGmnkCLjPiJH77vyNKHGgXlQTSoPQl9CsQcgAYeCoJjtCuMLW6oOA6Y9SEAx6jRIIaRz6g3Noa/XlANXmUyFNBjG/I2CUKMQYqVCvRvoSxcbA6H5yBpBqilOZeFNNGrWtPoAQUxopjpRGKn2j/VY7Uu+lOLj38t04DIhyRx0mzkd5lpEFaimS0R2oJY2iGkhOV0kjYkMh4+DKIUWy23vutCGShcBYtN1+bC71qy1oR32AfXP/9SHPS1dIo37KWdcWpZ+IAHEWpT4g+xw5/6fO6QOKPE6KHULIfrtWhNDftrefYyBp+r59fW9fz51zcaBEHxBG71j3yUZoP5PEbGefejm/fnfc6tA9wcB1IMDq4HcpS8hoUSMpwB11gJYWgjQGmgrIB4InfGOA52F2FQY9K/IjIAYzCiIihpAKhbQ2mPG6kUQDOtLBGAhlG7haA5LCODGAPHHhCsaNV9/Rga4alEUGh4rJ2PBYuxoSWhIQpkQaKRDUDgZYW/Dyu0IaKWTCqu4BkoIsNWJshZYMJMiCiTnq475ow9YGan8bwAy4HAtOi/vXaEgUuaRg6rPIoEGIioPI6dPV4AhY+Bq5LKodFZlD0uggrB/KWXNtRa1EHGqJlfYywQDJ0waIXFGiOEuNEDnE0PPiGBQaxFP7OIa84Or7gahzcExgQfiovELD7kWjykoJWaqrgqxyGOTlddQJc32UXkQNaTRwa+fuQCGNyCLnhApNcVocpBFBQQDZN+F8Cl5795baXUijduGA6JdtQR2RN84HMq+/IWldIY32Rfrc3+qUCY4P57gUBAvRV/zfdwgu2yhdR1F3fyt+K/uV7f2ub3pmXIN+5XngcHleRTL0b3befUGQ1aO969MXhb89X5wcbaLfIo2cQN+bjIfEsuEm3yCkxpWeOqERgjQGmgoGewogdYFRWxwG3sCJcPCoJfIbOJCZtrzIMtAYyJFXZLNMHFC/1kC54nkzGjxZhIm3yWDVhog6AoZL2BHRRYAQ3c6QsCWNokYxjEjj17/+9Zwz1VnSSNlA2hAqoSPqLYNvkG1koELUePlIIHWMmoCkMeZCbbVAaLSt0CpyaQBBWuVGNQJ9ifqBIMmTMhEGaeSs1Ia4pUxQpQ3YyJVPfV34rdG2KuFpdaXsCvEZnGpTAThFQpeIInVF8Rw4P2Wzkbb0LBhIDayIoDo7HhWn9tr0d9si3pRNbWAg5lA06kAh9YgPcqK4NveiM6QRSvSCEkTNcp+74sh1FrWkURpOV0kjwu7Zk3+LoCONnkGksT3nEgGTsmMfJAppRLjagn7p+dZ3FhdpVD8qMIfY88bB0l+XFJDL8qIA/ZKddh0cPQ4QgsdxdE/01XpgM/R34xV1nY12LGSRsk7N1fcUoW592HPuXrlnPRVBGgNNBYM9VYP3ubhIowEWaRRaYSiQL4ahrYEDyTNQMqSID9JoGRAEqC0SQRljcOS0IAEME7LnOF1RBhkl9eChIrvO0WjIdGmi5I4hXUgMwmBgZDw7M4HBPgYU+XCS9d036QrO0cgacRQAxlnSPtXvP/7jP3LelLys1oi/AZ26TO0wy9o9RzCpFu0pNgUGGSTVAIhUIakGZANI7fmQH30cIZZjSC000Ftyp9F76/qolWaVI472p3TW1hWZFarTjxFGeYLaUk4llaeR2dOIjrCu8wi7uz7Ha02Jda0IIoJmW6qke1BIaiN9AWnkfKmvY1DtXUPtpJtGob05gNobaVwcaSOdgXvDni1O0ug69FG2Rn+jmpVrrEcaTcZiq9wraRTtkUZqpjCrNBEKHZInfNuZZ7uA/UWmKNOcEM9ro6sVdAZIo9xzDkn1rGkE2/PL4XI92q2RflZIo2NQGh1TOgy7hRS6r8YSxXHZLc8c57It8aEnIEhjoGnAiPDKGDCkiydswOoqkEbeIOPIw6QaMlZtKYCFNJZ62M9EGEpiW4SFJ+6YcmF47oygQV2orSveeCGNZmdTseTvNDLQ14IRREgMMJLEtevi9OqRaQYRuaDmUtsQGYNXZ67fACv0ieQhzIiOPCpETri0HgwQlElEEWkU4hZSRWhaI2b6nvbQT5ALxFFeqhnVjagOBjuqImXasifIoL7jfLUDhPMgk4gDVda27m+jOZTupX5RCK7QHoVDX6uFAVCKB/LtnlBtPQNImbrVy9mCsj9ngIJc8uYoTbUhZ/eNwqLtEEZhQMREXfXdesqtgRb5NQAjje6bcxvYO6uw60cUJm3M8XI9nVUatb3jIbbWlPTZ6GSpQhopsVSpxUEaXYfnAWnUF9wbJEzd2juue8RWUY8500h1e+FppFH6DaXRPfGMID9dIY3ao6QzeMY9e6JCSwqeQ/ee8i7dgb023tSb7NIWSnha2hI1ndBRnKO2xhbjR2sz1HsSgjQGmgaMiBwUAwx1AgHxYHcVSCNvkMETNkNmKGBtDULqwRO3jIUws7pQJw2SbZFGg7MBhCHmjQt78DqRs64MCkiema4IBrXTYFAbgmwEBjtGE7EzaFFxESIqDMPf2UG0QJ3Ujfdu8FIoKganRnPZWoP2c93IH+JIyZX3VM/oajdKCnVM3pLwtuO0d9/dJ/fYgE79QzLlH8n/qofi7MgPQ5oNxPInDYq194sq7RrK22eEzw3eCHFtjmBrcL8QMIOt60KGEGSOTmv7qpt7jiyaxOAZoBQiUoiC/t4W3DvqNiXFBCE5jZwoeVsIUGuDo2iBwVM6gLZ3Xg4PklovLOf6DeocBITTOami7EJn4fmnMCH0bIpBvaPQ5gg2uyB/UJ0o3yIYHJRGgGSwEdWksSOTn9oCm0Sl84xwQBB6ald7x0VW9T9KNbtYL6fRM0PttS0yrw9Q/btCGj3D6kkZ1R7I15JUGkF/1R/0s65EgAo4DAiodCpjRVnBYHEcu7sQpDHQNDBAGfgQNMSLWkEV6yp4gwYNIUfhG8qFvKa2BkvfIwqSlxkzBtIgwcAZ8FsDA6iulAzkxqAsR8dg1xXSZEBCeIU9Eb2ukFD1oNgw0sJLBj1Knlw6bdSVkJ3BgxePqBlYkGb1Rkq7QkgNZAY06i0VxXGRHfenPbJT1C4EifKHdBuU2iNJCBcipH+YlYz4IhmtKXjVcO3IoW0RJPvKcUJA9ZfadnV+Az1lsqyth6QaxPWxemqcPmFw0p+diyqHvCDKrYGyyfFwPcK9yBiS6nwmN7hHrUF/cUwKkP6sLV0f4l4cqNZIqoHUtSHQSKOJOkh0mUneFgy0+qJ+bl/KpnpyvtojNPVAvXIN+oB7hLh1BJRmDpGJRhxahFY7iCY4LgLSCApprA5PI41dJRj6GCIrPK0v6Q+co/bshD5dng+OhzZuLzytj+srVOMvf/nLue9RGruimDkmVVnkx/NCaa+dNLYkwB511Uku8AzoF1RGTgnHr3YFg2ZDkMZA08AgZXYwRYhxYtQWh9JYcsgMXJQnxK69gcOgjuwhjZLwhWKQIQNaWyofT9zvCBnvXWgSUe2qATFYOg5ViXKF1LRHluoB4TBwIinqaQCkDgqXIn2NhtpqYUC0vzAp0qjdDDKdDf0UCOUYmHnxBjj3TxsjLW2RKwMP79+gTsWTE+meG/jrhTgNnAZzZE77UBAoZG0NZgZ8fZbSh+hQxgzCnAwOUHswo9hgg9Qa7PUzBJlj0FqYWhvrT8i4cJ5JD+4jEudYbeVJOZZ8XPdErqkQM+dJm+pT1OfWQvDalxotlI0kaUeknYqondpSRNUDAXA+1+acPpFx9825aveVcuGZFCbl0Kife0010zcbJWatgXrFYVAfiqm6UV/dU86Sa0GOEVrbqj9F1IQlqpGwrPvpmeYQ6lOuiTNJFW0r+tAaSgoL0ogc+7uroUr3t3rJHfcLGWuPNOpj+g2nAzHX79pTTD03cliRxeqcxq7UvSiNnk1OcSNKdE+C57HYJ31L4SzpU4uLlHYHgjQGmgbIVVEaGcBGVJ5GUEgjI1+Uknqk0WBBzaE0ClNSGBjitpRGRpWKx2u2PIxB3f4Ur64oCUgCZc1AgJAZdClHzlcKj721Ur1N2Q4ZdpwymJvUgORQkuSQOr7B1ECEIFcXBLC6VP+mTgYRoX+DEOVAe3UVBhF1QmwROUSCR49IC7EhG/oNA+7TgK8eRS2kclGt5Zc2EmZ2PmRXH9FfDI4UOeQJ0ahuF6TK/XWfC2FEbA0eBpL2BmGDCgcAcaAQUeQM+Eika0MmkCvnK+dEbKjXiJv7h1hJnTDgy3Fsa6BC0FwXFUTfpOA5l/+rK8IrBE2Rcy7XhQgV5dgzgygJf+rfZpm2R5TUFUHX5uqqXeRTak99z/6IGgdFyBchRGoRWE6M63J9hURri7aeu0agHTkR8s4cU6hcOBcZNGvW/UOEtbvJHvqb+029FUrWRp4RJN19sr6f4r6pHxulfbWb4nzIZ/V3iv6DsHIA9WHOiTbuKmnUNkgxQifdgVPFgW3P7nB02FnXwL6xMerXFjzv2kt/EwJXfxO32JTOwnVTRLWHfm82vjZrFmhfL3Cg4usj+pf+hDS25VA1A4I0BpoGlEbhGsZMOJLiuDhIo0HJgIA8GCwNGgbstlDIqwHBIGawQ1oMrIx/a2A8hbwR3UIaDcbO05VBAVFg0BkkxNHgZukLxEgxwFGZSqEaKdXflaL+vHmEygSML3zhCznUJEeJ0oWoIwUUVgqK8ygUBvlMBtKy7phP35VtDIauF/lEGqnEBsSugmF2/wzmFAkkRPF/iptrkmeGoBkI1QnRQeIoYxRrYXgDHmJbD/qg7VyTmeDUSoMqMmzZFkoCVccAp41cs9+RImTH9nJhEVREvS0YVAwuyAz1C8FF5gziZnfqe4iAsKOBiNqG9OkDcgWRKsq5Z8Q111OIkWohdERFX3Iex0AyKI7Ck87hfAiVcyJMnhl5kNrSdkX1a08953Qh74gL4kihU2fXqI/pf0LVSJli0PVMulfaEEn1/FDk5G4ilurfWWgbfdg59AvkijPIsaH4cQz0Kden7fVd/YvKrL7ui6WGFK82/NznPpdnx3uG3HvOFqeUo6DtEHvPrE/flUJFde3qIA/V/fR8dyVyANpHmgm7ox8iYWyRvtwWODvFEVMXda1HGj2DbCFHE2ns6uLe6ie317OFdHkWWlO8eyo832ycZ0c/0l/YZypuVx2B7kSQxkDTQDilTHxYnKSxzJ52TIMST7w9QmNAREQYACTIfhQSyhklpjUUomk7uWMGPQM/0tjZHEQQnmbQeeIIiUENCUJOETyfSLYihOb8ir8pZL4rRS6VNjVIIgJf/OIX88xiqolcNyTCIIIoG1CRJoMn1c057euYju3/zu93xUBrsHLdCsLRmQkHbUHoEJEroT2DvIFGHZA5gzQ1WD6XdkIMDOi2R3INzu2RuFogdM5XFMcyuQchdmznd52FnOpX+goioB80QnI4GhRt5Fd7I02IFVXLcali+h4yICzq07ndI+d3T9WRateImk0d1B8Nzu4Z5ZB65nzORUVCkpwDkVCHQuL0P/25I/eUCoy8uDeIsXoLp7tGJFL437nVg4LsXP4ug29RP7sK9129PUfa2bUp7pdP/UWf9zfiqF+5Xr+551RWIX3PyWc/+9n0mc98Jjta6uue2E/fRwgRIMTeeTyrvitFG+gz7rO+iWgKgXeFEAObhOyrK0LnXOxme6RRxMGzUeqibdrKbQU2jOOlP2oPjgBHtCtRFGSZI8POeG45tM1EGpF1jjvb6PnxTLIXnEn2qitt050I0hhoGhhETSZBBBgnBGVxKY0UIoOAAcqA2V6uJGNWJsIgKEgDNUH4mcfdGihHiAniQsUxkAh7dfUNLkijwcVAyrjL8WKYtE0hcNUFYaQgFGJXTSINEgiz+lk2wyBIYaSkUE0M5AY129jeNbseBFDo0IxZxf99h4T6vRShVsWMYwNAe+HZjsLAishRjCiJZYKSUggAkuPakGKDODWLUsVpQOo7EjIS6kVYKKgIsUEByaluK+dCIil+CAGiQ8FpVDlSH/0JoaEq6pcIGxJKEUdKEPkSEjVzGalDSih42sLg1CjpcD59sRBw/QRB0m5FvUQiEVQEz3UhBwZ1pELIuSP5eyBU7Rl2fe6b4yGI0gakR1DvtCnC4x5ygqh1njUK4eLIDXPdbAvCTEF1n6h+nk+EVhRC8bwj/Qr1U18v6RYUPPeB0vj5z38+3ws2CjH0PNhHGzmGfanNvvO37xXn1eaIKaJKpRbebI/c1YNrc0/YN6qwvsM+cL7bUoO1KbvELrjXrkOd9YvWnhHfcQCQIdtqC/cRYeqII1YL/bZMHmTXrHPaTKSRfdAm+khxIvUHfas8K621Z09HkMZA04AB4nkapA1klBTGr6tAGhhVhpqSwai2R0YN+iVXhYEvBFb+TVu5VQw/Q4yYGXApFcgexbIrpLHkNCIlDKsBSohQWFpoh3GiyMgJE5b26XufwkfUUdtQBYQxqUUMHLXAwFdUJkpLMXiUOfsZuA20SI3i+nzKJXRf/CY3tBTfI03y66gWCMPihEGGA+C61BPBUOfSNoi1hHoDM7KH+AuTdlbJYfCdDzlzX6lHiI1+hLQ6F0KFPDufe92ZsBTiqL85hrqXPFqEWN9DBihalEADrH7l/iDRnSEcyIQQPBWQQsU50H6IgHMjpa5Ln0e8hSXdWySuM6FUSpj+gCAgT+6ZNvScIMnalKOCVCH5HKW20kC6Av3RxIUy8cV5ECXfUfz833eKbVyzVATOl3bhnCDtiJk8TTaKyu35cjz7lGOXUr5T3GPOlGtFMDzLnqeu2Adty5YJkXJiOBpIjGe3tXvlWZA3KB9RuB6BR4pLfqXj1RId7UY9R7LdM9euLSjWno/O9AnQD9VTX9P/mo006tOeWc+/Z8gnZ04fZ289n4vD6VnaCNIYaBogjcWIMMgeRIa7q5CULnfKACyHC2ls77gedEayvHuaoURQDGhtLayt7siaUIWBEIFZHKTR/ogeYkTNM9tQ7hGiUYw74+scQkg+1R+ZoK4YJGxnewTUIIj8UHYMgAYYg7UcPcqBcKlrtH9PNXgGFoOt9jb4ybUsOZfItFw6BntxgdOBGDhXyeP0qb2Qc2TIANIVVcG9osw6j4k47gdVTK4aYkfREB7kGCDvi2NwRXARJc+ca5On6pqQcn1dX0NIbNOWwt4ROB8iXxwYA66ClDunZxLJ7ylAhpA9Tpl7gjxTQUVCCtl1fzqytqA+a38EHeH0vHVWafR8IrjqwGZyLqjhQr0ImH5ba3tKChCHGFFDNNnFElZ1f2rro28ju5wI2yKa7CK7pL8K03YG6sIRZ4NKnZuJNJZ0D9egHdgBoofivrqWII2BwBJEIY0lYR1JQt66AgM5o0etQ5SEwhzfedoic75nAITThOgYY6TRwEZtqSUH/mZADLoMoDwhA4rwk0G3K0nRCEKZwcmDdZ7OevbUFIaZmqUNeMX+poBQUBGDzg5gSxPa2z3SrvoMJaQUf/t+cRprxyrn0kblXP6P7Bn8OqtmVsN9dR7Hpfgg74p74+9yfcUxWBxQ7+pr81lKubbO9rfWwMEp5yrtWH1dPQ2uXTuU+iL2SK5nx/ONADdKdN2zQhqlvVDukNK2wsj1oG7sI+dUqFkuI5WY4ypPlnJYq9hqZ3XgKEpBYQeo19JKhOjZPddbDdcsvYDaTiU2kcp+SC8yTW3sDLQpJ49DzL5xIJqJNJbnVZv69Kz4XBLPzdJEkMZA08DDxksrpJFh7sqbIBhpXrBjIoCS8OXjCDVRHpElD3c1GACGnAETRqLG8caFIhliYVjHLIO2QReRQw5LDqSQr/obHIR621InGwH1hbE2W1GIvbMDDKgHEqpOBjvXX/L9AoFAfXju5bJ5dhSECVFoBJ4zhI0DKu1F3iNC1llywfZQOdkkSpeUBaqoZ5va7tjsWTU4hZxHhFJd7OOTjaSacbBrHUekmN0oCnFR2e3HPnc2lcB+CDibyb4125I7yyqCNAaaBggcY1ZIo3wqBK6zYFTlKzFy8iPl7gkr8WwluQv1UXCq4W91QAB57jxgRZ2EqxlLxyyG3kAgpCNkKa+IJ15yw4R8hHXqLYfSHgwICC/DKgzVVTVGGzPMVJNAILD0wFaIcAjzIkmURqH/xaFSAwXesTjfSm1EpBa2VRpVrSmDCCSnmf3oqrPJ2UYU5UcKd0udCdLY/QjSGGgaIETybYRLhIV54oxqZ8EYSvjnfQu9IH3ycISqhVt417XkiSHkoctfQlrNgLRcj+0RQB48da6aNMoVRCbLGnfCRWVWppy3riqNwtOILqNaq4x2BvUGk0AgsPjBVlAEi9LIRlD2GiVtyxq8RIBdtdqBiV8m+AVp7H4EaQw0DXjHZnSaPc3zlKyNwHUWyJHwjEkRJpQoVEEhFTN8EcrWcvjsI8EcYbOtOiCvPoWmeNzV4WlKou0du8zKdHz7dnaGa4GcJblDlpBBXtV5cSkTgUBg6QFpNLlIBELkoJDG3vo8C62b7IUwygGXX019DHQvgjQGmgZUv2JUhW8ojUhYd6EjitySUu/MwpNwL+xNJUUiF4faGAgEli44j6IenGKksTjFzTphoqtAGimNlh+y2oSJhJ2diR1YfAjSGGgayCe0fAHSKHwjNNyVnMZlAdY9pDRaJkfOpGT1RhPvA4FAz0FrpFFUoreSRlETpNEasWZkX3311Utkfc5AxxCkMdA0QBqrwzeWmOlKeHpZAGURWTR7m9LYlXXdAoFA9yFI46cRpLFnIkhjoGmANBajavaxiSTtvUS/N6AojdZfM6PbzO2YyBIINB+CNH4awtMmDwZp7FkI0hhoGljE2DI41keU02gWcpDGWXnWt0XDeeVdmYkdCAS6D0EaPw2k0Yxpk2C8nSZIY89AkMZA0wAh8tYVqpq1u8wujPD0P2dPWzPSu15jEkwg0JwI0vhpBGnsmQjSGGgaII3egWvSx0YbbZRnTzOqvRnesXzYYYfl2dMWwg3SGAg0J4I0fhrVpNE6tNa6DdLY/QjSGGgaVCuN1mks72btzbBW5PDhw/NEmPPOOy9mTgcCTYogjZ8G0uiFBd6gFaSx5yBIY6BpIKfxxhtvzDmNkqO7e53GngCvETz00EMXvREmSGMg0JyoJY2WFOvN6zR6+4voifz1II09B0EaA02DWKfx/wJpHDZsWJDGQKDJ0ZrSiDT21tcIIo1sWpDGnoUgjYGmQfUbYSy5M27cuDR37tyWX3snLOZ9yCGHBGkMBJochTQOHDgwbbvttnlVhIcffrjl1+5Ddy3hZfkwy6rJaZSzPXny5CCNPQBBGgNNg0Ia99xzz+x9TpgwIb/ruTeD0og0ymkUygnSGAg0J5BG9g1plLMtDeeSSy7Jy4pR3dorr7322qJSvpMT+MILL+T95UZ6P/6LL76YXnnllU/t62921G+KfRC2xx57LL8sYObMmXmVBu/Op3xy1H362/v6EVvv0lfsI/qjlHM6fyn2dey2indtO7+0I68NpLquscYa2b6ZBBlLinU/gjQGmgaFNFqT0JI7vFAGpjfj3nvvTQcddFCeHOSF/jF7OhBoTvz9739PU6ZMyaRxpZVWSquttlomjt74NGrUqKw8euvTcccdl//2Wf5fW7yP3n5WVjBRTgqL3Gd/Vx/HpyW7jjjiiEVl5MiReVt2ZfDgwWnQoEG5HHjggWno0KHZSfXpb7/7PPjggz9VynblvNVFfdorzl+iJyussEL62c9+lpVX4Wl57YHuRZDGQNNATqPFva3Ztfbaa6fDDz88TZ06Nb9uasGCBTl04YX2vG1edvGe/c6jfv3117PReeedd9LChQszCbWP7+1XXXzXWnGeUubPn/9/PPXnn38+e8u85lqv2vflt/J72ab8pviOV86bV4q37jck2bkU+02aNCmv0cjAXnzxxUEaA4Emxccff7xoNYQ111wzLbfccpk4rrXWWtneUdz8f7311kvrr79+WmeddfJ2iu+ry+qrr55WXnnlTD4RrxVXXDEXf6+yyir5uI6n+P+qq66at//LX/6St/F/27VWbFv7d21xTHWoLX6zj+O3Vpy/FPX+/e9/n5ZffvlMWu+5556IpPQABGkMNA0Qvuuvvz7tsMMO2QAKWVh2R1j2iiuuyOELC8AK6fjOG1LOOOOM/Gnh68svvzzvf9ttt6U77rgjq5aW8LGffBnF/3m0pZS/r7rqqnyOyy67LJdLL700F+ei8JXznXbaafmd2BYe91o/b62hiI4fPz6dfvrpudjG934v29nG94r/+87scNcnId4xXYu8xQsvvDCfz7b77bdfDmXJ8QylMRBoXpjwwjnkCFLkOIOiKvL5rE3L3vn/XnvtlcO2fhdhUHxfXWzPuWYrt99++/zpVXxK+b/j2a4cg+PpN/sNGDBg0XlK2XvvvfN30oMUf5fvy3eKbUrxW9lOoZw6djlnbVGfUif7H3DAAVl5ZHs5yr11UlBPQpDGQNOAOnjnnXdmI8T75I0iTNttt102eMWwMnxyHv224YYb5rLpppvmEIffGS4GySfD6/8m1ziuvxldxroYPds5NuOLnCmO5TzO65iMsHP26dMnKwCUgXXXXTefWyjdb2ZEKhK7LU5e1ALF//v27ZuXElLK746xwQYbLKq/8zG6zuk4PHrKgONTGj/44IOW1goEAs0EE07efffdHK2Qq3z33XenadOmZYWN3bv99tvTXXfdlSe/WdSfKun/rRVpK9OnT2+1OIYiSmO76n2cr3xfchmri/Oqm3NXf2/b9kr1/vZ1jNZK9TXYXt6k3EjRIzmfge5HkMZA00DOD0+c8oaMCWcIr5TQTXV4xG/UyD//+c+ZYAp1+E6IpBC6QtQsHosIFqKJ+Pm0rA+Sh8TZ1r6OIbzi/8ieeiB4juNvv5VwUDmfczlm2Q4JVIdC+GyLALsGv9nGcR1PqMmn/ZFEdVJX/7et322P2FJEgzQGAs0PazN216zlQKA9BGkMNA0Y0TLDUMK2RG1J10OGDEn777//olAJ1VDYVh6M8IZk7VIkbdtPorbcIXmRksFHjx6dE8Mlj/tOcri/fS+pXIjEuezvfP4vydv36mKfESNG5OOW4/u9nMPxJKD7rE5Ql/BdEsftb5vqZHbb+1QXoWoh61Inx1F8byY57xyxDgQCgUBgSSBIY6DpYBLKnDlz0qxZs3IRxiihmhJu8XcJi5RtqkMlvrNchOOUpSIU4RDf+fS3pR/8blmJchyflqIoy03YXvF/35Xvy2+OVZakUPxdzlO9j7/LkhVCMj6dv5SylEWpU6mjbSmwJupEzk8gEAgElhSCNAYCgUAgEAgE6iJIYyAQCAQCgUCgLoI0BgKBQCAQCATqIkhjIBAIBAKBQKAugjQGAoFAIBAIBOoiSGMgEAgEAoFAoC6CNAYCgUAgEAgE6iJIYyAQCAQCgUCgLoI0BgKBQCAQyPjrX/+aXnjhhfTss8+m+fPnp/c/+CBeaRhYhCCNgUAgEAgE0rvvvptmzJiRzjzzzDRmzJh09TXXpOdfeDFIY2ARgjQGAoFAINDL4b311MXzzjsv7bTjjqlv377poIMPTtOm3xukMbAITUkaP/roo/Txxx+3/BXoLD6pNOH7732YPvjgwzAKdfDBBx+kd955J/3tb39L7yxcmN5///30ySfRZoFAYNnAG2+8kW695ZY0/NBD09prr53+/Oc/p8232DKdfc556eWX52VSGQg0FWn85JNP0ttvv52efvrp7BEZyHsiPvzww/Tmm29mgtFTydhHH/4jzX/lb+mRh59Kzz33QpDwNuD+vfnmG+nRRx9N06ZNS/fcc0+6b8b96aHZc9LL815JH0W7BQKBZQBPPflkOuP009Oee+yRNtt8s7TJJpukzTbbPA0ZcnCafP2Naf6CBS1bBnozmoo0vv76/HRLxRM644wzsoQ+derUtKAHduR58+al2267LV111VXpgQceyInF3YmFC99JTzzxRHr11fkt36T06rwF6dab707nnjMx3XXXPeFFtoL3338vt9vkydem8ePHp9GjR6fjjz8+jTllbDpt/BnpyquuTnMefaziHLzTskcgEAg0J+6///50+GGHpQG77poGDR6Uhg0blnbddUDqt3P/is0bl56ZO7dly0BvRlOQRmrPe++9l+6+e0o65JBD0tZbb5369euXjjvuuDRnzpyWrXoGqKEPP/xwOvHEE9PAgQNzQvHLL7/c8uvSBzI4e/bsdNZZZ6Wbbro1vbvw3dyewg0333xbhXxPTPfcMz1IYytYsGB+uvTSS9Khhw5LBx10UDqsYlCPOuqodPDQoWn3PfZM+w8+IJ13wUXpuedfaNkjEAgEmgyV8UB07IYbrk+DK2Rx0KBB6cILL6yMFzdVHOXjK6Rxl3TIsOFp+n33pY8+/qRlp0BvRVOQRjmMwoNjx47NhHG11VbLORe77757mjJlSstWPQPI17333ptGjhyZdt5553Tqqaeml156qeXXpQvk8MUXX0wXXHBB2nvvvdMxRx+bHpw5K33w/vt5GYXXXpufHnvkqfTC8/PSx2EM/g9eevnFdNpp49J++w1MRx99dJo4cWK6eNKkdNgRR6QtttoqbbTJpunIo45OjzzyaMsegUAg0Fwwvj733Nw0/rRT04AB/dOIESOy6vjqq6+myy67PPXrt0tlLOufzp94SZo3//UUqdy9G01BGhGxW2+9NQ0ZclDaqjJYb7bZZnlml8/TTz89kzIdvxr/qPTs115dkObMeSTdc8/UdNddd6X7Kp6S9adq8wzlRj7zzDN5qQHbyVubNWtWhVS91rLFv2AyBHUTMRQe9/n444/n/EVQ1zvuuCMrU7vssksOpb/yyiv5N3j99dezEjl9+vR8LsdwPMctKOtkzZ07Nx975syZeXv1813JP3TdHu67774711ld5HuW3xcuXJhuv/32dOCBB6YNN9ww9dupX7rk4kvT/FffTO+/91GaN+/V9PDsx9Jzcz+9pIK8UXVSP3l8zjF37jOV4/6rjf/+9/fTa/PnpSeefDzNeWROmj37oUr97sttrL7q3WhY/p9G67l8Hs7BW2+91fJL98IaZedfcH4aOvTgrDCee+656exzzkmDK+259rrrp9XXXCsNPWRYmv3Q7JY9AoFAoLnwbmWcmDLlzjR40P6VcXXDtO+++6TLL788CzJjx56aNtl087Tm2uulA4cOT9Puuz+9/8GHLXsGeiN6PGlEZszquuiiiyqded80qNKxTzrppKzkbbrppmnXXXdN11577SLSBojbc8++kK69+oZ08slj04jhIyoD/9A0fPjwdPbZZ2dCKNxdtn3ooYcyuXNMZE8I/JhjjklXXnllJjOFkFrDCpESeqY8KULkQr/IEpJE5rcNota/f/90ToVkIJ+InPzL66+/Pp1wwgmZhJRCjUT4HB9M8nFuoW3q6qhRo9KRRx6Z18264YYbMllEHoUQeIVyTw4//PBcXMcjjzySZ/ciqLbZZptt0qqrrpI22WTjijd5Rpr71LwKUXy1YhiuSmMq7XPLzbemj/7+UW7rBQter5DeO/M5hSm02T8J0zmV485JC99dWGmPD9Mbb76S7pl2exp/xqnpiCNHVs49Ih1xxOF5W3U95ZRTMuHUzkL27QFpl6vq+q655ppuDecXaAtk/+KLL859R1uUPrTnXnunDfpslNZdf8MctnkoSGMgEGhSvFkZX88/79y09VZbpbXWXDPtuOOOeUxh6/bdd2Baf8M+afkVV05bbLVtmjTp0rRw4T/HqUDvRI8njQsrROqBmfdXSNzRORw9ZszJWQW78847M2Fcc801MsErap4w69NPz00XXTgpHXTgsEqn3z8NPXhoGjJkSCZx2267bX4gTFBBGClbSKhjKfvvv3/ab7/90m677ZZzEhFCIV6q3c0335wOPvjgNGDAgEwsEUZ5boceemgmSRRGs6Ypicic851//vmZLJL6L7300kw+7G8f5BHBQlRdA88OcaTS+VvephD3AQcckAktQnjjjTfmSTannXZaruNOO+2U64Qw7rPPPvmcCJ88RmR70qRJeRbcSiutWCHZG6fTx5+Znnry5fTA/Y9V9jkqbb/9TunMCeekd/72bnrr7b9VSOlNlboNr3y/fT734MGDF7XJ8SeMTrfcelN6/vmnK6T10XTZ5RPTPvvuUfFCV00bbbxh3k5ba0cqq4kj1ENt1x4Qam3rmiiv1aprd+G9he+kGfdOT8dW7sPue+yRHRb3SduOqlzXHnvunbbYcut0SKWtZj74YMtegUAg0Fwwvo0cOSJtsMH6afvttsvjifHniCOOSCNHjEwDKuPuehXiuP6GfdMpY09Nb7/dvRM7A92LHk8aX331lXTlVZdXOvJBmcBcccXlWUVDxMxkXX/99dM+e++bZsy4P338ySdZ6bvlltvTkAOHVkjXrhUSMyxNmjgpXXfddVnJQoQQLfL7U089lUkdooXIUfWolmY9I4RIGLJGMUMykQbnK8SMEujhsi+Cd+yxx+YwMfKHNCJ18gmRN+of9bFPnz6LJvFQPX3af/PNN8//f+yxx7JqiaStsMIKeXvXSaF8sEJOnnzyyTR58uRcL+2BSFLpXMeee+6Z1llnnXwsSiXlE5FV3/XWWy/tscfu6brJN6TXXn0z3XvvrAoZPahiKDaqHH9MevbZlyrkZ3al3iNz2N+1qzvlz3Wqzw47bJcOO3x4uummyWn6tCmV78enHXfaNq22xspp9z0HZIKqbpRY3qrzUoiFeevBvRB+b2TbpYG5Tz+VJow/LfWvkN9ddt4lOxYIu1SACy68MO07cP+02eZbpaHDDg3SGAgEmhJSgW6+6cbKmLRj2njjjXL0zFhTxjHizMSJF6fBBxyYNttyq3TgQUPTlLvuzlGsQO9EjyeNTz/zZDr99NOy6ockyStDwKh5lKltt90u7bhDv3TO2eflJWXeeOPNSiefVCFQe1e2PzBdcP6Fae4zc7PahXAhi0gQZQsJ4FVRHxEzCp9QKVKKoNmWOughGjduXCZwa665Zq4L0khdpDTusMMOmWhRERFB6iSCuMcee2QyR2X0ANpurbXWyiqch/Pkk0/OiiWC5dgUReFnxGuvvfZKyy23XFb8KIvyDIXJqXJC2XI5XQclz7Iw2sVxVl999UxsnRdp1FbCDELUiOyDD86qXOOHadas2ZVrH5b69t00HXXUqDR16owKwZtUOcZOOW9UWJvipz0cf/z4cRXCvWOF4PavtPvYCpm8Io055cS08y47pt123zVdcumkrLLaXk6ja3FO96iRiUCui/Jbm2/aHVCH2Q89lI4fPSptV+kbO/fbOd9X7ZAnZJ16atp6m+3SuuttmIZUjOjMmUEaA4FAc4Gdm3HffenQQ4amvn02rIw5e+YxkcjBFpfy0ksvp0svuyLtu9+gtNW226dDDh2Rpt97X8tRAr0NPZ40znl4Vjps5PAKKds0EytKIRI0cuRhWcnr02ejtOkmm6WDDzokTblzaoUkPZEmTDg77b33PunYY49L98+4P+frgdw6D4R1FOXNIWhUPjOykS6/FVAseVMIH4KJKK644oqZNFL0kEI5bkif0KXZyULE1DmkEcG1HbKBjF5yySWZzCGClECkSpicgmdf2yKSV199dSaqQr22FyKonkgDCDPS6DfqJLXTMTbeeONMSk16cV55nvIjEVzkU0gcofuwYghmz344q7Frr7V+OnjIsHTttTdU2mt02mKLLSvnHpSJacF7772bbrnl5sr2gyuEd+fKdkelSRdflE44cVTq379f5bhD07Rp97RsndLzzz+fr23LLbfM6q7wR7OBkk3Bdd832mij3E+kEow6blTlnu2fQ9N9+m6cBlU8cCp3IBAINBM46pddMiltvunGFRvXpzKmjM92rxb8+BdffCmvT9tno03SVhWH+drJ17f8Guht6LGk8Z9vf3krTb7u6rTHnrulvn37VAbqLTJRRNiQNcSLMrbJxpuknfvtkiaccU7FU7o9jR07Pu03cP80evQJ6Yknnmw54j/Bc6LAmZwiFC1UjcSZsFL7wFAcqWfIpXxKpJGiiITZnhonlI3oUSWFhBENIVmk0T7IG3WK8rfGGmvkYyAiyCUiaVvH8bd1sRBCn64N+aNGIrDgE9l1HtePaCIzSCvF1N8IDnKNuCKNZmHLndxuu+1yu02dNi1fl/MMGTI0rbPOBumwEUelW26+s0JCj6mcs08aNGhwnhxUQD28++670qHDh6VdB/RPx1RI46WXXpxOOml06r/LTpX9Rqb7779v0YQhM9ERaoolNbYZSSNQd91bzgAVGTEfOvSQSnuemMaOOy2NGXtqOn/ixPTk00+37BEIBALNAaTxzjtuT8cde0xlzDwlr4DRHqZPvzeNPuHkdNwJY9L0GQ+0fBvobeixpNHbOGbMuDcddfSRabvtt01777N3mnDmhLyEzIz7ZmRSI4R8/vnnpb322rtCinZMI0cekc4998J00olj0sB990uHDhuR7ppyT/r7hx9nEip/wz7CzdRDZM2kDURQHh6yYzsF0aG2IYzW50OC1l133by98DEyRpl0TP838UTuo4kciCCSIaePgonoyak0IcWMb4TOdwipT7O55R6a4ON4cvsQy+WXXz7nLiJtgOwKc1NakUDn8KYSx9YuCBqihmw6h+2pfoU0Dh58QIX83ZNnND/88Jw0rNI+W2whhHxW5dxPpXHjzqiQyHVzWBlxZVQUdbzsskvTwP0GpgG77ZpOPOn4dM21V6QxY07IIevDDhue71UhjZb9QWLVRZ5oI6RRqKQnhKZrIa3B9Qvz6w8PzJyZ5j73XFpQufdvVO7V65U2fq+F1AcCgUCzgL1l315/fUEedwgq7cE49OqCN9JzryxIb74TM6h7K3osaaQyXn75ZWnAgF3Ttttuk0YfPyrNemhWnl0s3FxN7i688OK0yy67VkjarlldPPmkMemAwUPSHrvvlcacNDbdc8+0TMwQIbmLJrSYQHLFFVdkFYnaSIWzvApigLQJEdtW6HfChAlZ8UMYTWJBzpBDkzeQRSQUAaU2mijhuJRGRA2po2qaSGNyifxJIWXL8iCJJr3YT84kBVHenCRkYWukEUEsywNRCOUw+o46KoRNoZSsjASbiOP7LbbYIhNdSiMi7BoQuN1336NCMG+okN2/VdpjTjrkkOGVbbdOE04/J730/Gvp5ptuy8olEm0fRNb6kNdee006+uijUv9d+6f9Bu2Xzj7nzHTDjdemk8d4W8AOlfY8oLLt7YvILWWVUoogazekuj0wXkLwlhEq19oTgUDHu6YDgUAg0FvRY0mjfELvl5ZDJyyIUPGIWsNjjz1VIUDD0vY77FAhO8emiRddnMadOr5CqiwXM6hC0kbltRCtIehYyJaZvgifRcMpcVS7sqQKsij/TwjYfmWZm5KraIILsuk321rOhyKI/An7In0myMi/RAblUCJFiFwJW8v5s688Rvs7vzxFpBAJRAyRNwQVWSygbjqOiTJIqP2dw7Ec22QbCqe68CJNQhEi990ulfqce84FlfZ6rkJ6H6ic47C03bY7pAnjz0pvzn8rvfAcAn5hPo5Qtzogoocfbqb2/hViPTidfsbp6Z6pd6WZM6enM88al/bca7dKOx1UIY23LSKNZoCbdKMu6lZPaUQaqbTqTKUsimUgEAgEAoGegx5LGoVukQjE5ZRTxmb16pNPWld55s9fkBU3ROXss89JMx+YmR64/4EcGkaqyjuD80SGCim0rXAjVYsaR+1DABE/x/BpkgnSKgxOurcdJQx5dSz1Qhxt5xzqKoxJCbUguH1t53u5kogQ8njZZZflfeyvXs7nkyJJ5USW1Y0S6vhC4SWnERwHsUTG/G5/53FdQuwUQt/JxUPi7OsaEONDhg6tkMbz07QKYbxryvQ0/rQJaeSIw9PVV11T2fbDrOBSJhHqI488KpPmf9ZzZBo9WrudlxXbd975a3r77dfSzTdfk0aNPjovvTNnzkOVuv0zvKEdkE910V6tvVmnGkgj8u6aKLjaOhAIBAKBQM9CD85pfD+HapEI6l17C0TbVqhYoq73AJvAsHDhO1m1QgiFWeX8CQnLaUTqqsOglpZxDqFliqLi//avJmwljIq0OSaiQxVE9hClAsc2Y1qY2zGqz0X5Uye5ieqkUCZtX8iS+quP8wjtCsNXA6FGLLWNOqiv/7s2s6P93/GEUwGRRRzvztc/K8195rn07Nzn0+yHHk73Tr+vQhTnpn9U/oF95EHed9+MXDfHvvPOKbkuzzzz9KK31qT0SeVanksPPDCjQujlYr5ZaZ9/1tP1uh/qgoT+a5/WoV1trx18VrdXIBAIBAKBnoEeSxoXNxCTRmC7jmzbE9DRenRk+6V5jc7VU9o0EAgEAoHAp9FrSGMgEAgEAoFAoPMI0hgIBAKBQCAQqIsgjYFAIBAIBAKBugjSGAgEAoFAIBCoiyCNgUAgEAgEAoG6CNIYCAQCgUAgEKiLII2BQCAQCAQCgboI0hgIBAKBQCAQqIsgjYFAIBAIBAKBugjSGAgEAoFAIBCoiyCNgUAgEAgEAoG6CNIYCAQCgUAgEKiLII2BQCAQCAQCgboI0hgIBAKBQCAQqIsgjYFAIBAIBAKBugjSGAgEAoFAIBCoiyCNgUAgEAgEAoG6CNIYCAQCgUAgEKiLII2BQCAQCAQCgboI0hgIBAKBQCAQqIsgjYFAIBAIBAKBugjSGAgEAoFAIBCog5T+P7Ynfra0veQIAAAAAElFTkSuQmCC)
A block of mass m=4 kg is placed over a rough inclined plane as shown in figure, The cocfficient of friction between the block and plane is s=0.6.A force F=10 N is applied on the block of an angle at 30° The contact force between the block and the plane is
![](data:image/png;base64,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)
A block of mass m=4 kg is placed over a rough inclined plane as shown in figure, The cocfficient of friction between the block and plane is s=0.6.A force F=10 N is applied on the block of an angle at 30° The contact force between the block and the plane is
![](data:image/png;base64,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)
If the unit vectors and
are inclined at an angle
such that
, then
lies in the interval
For an interval, square bracket denotes close bracket and parantheses means open bracket. Close bracket means that point is included in the interval. Opem bracket means the point is not included in the interval.
If the unit vectors and
are inclined at an angle
such that
, then
lies in the interval
For an interval, square bracket denotes close bracket and parantheses means open bracket. Close bracket means that point is included in the interval. Opem bracket means the point is not included in the interval.