Physics
Fluid-Mechanics
Easy
Question
The tension in a sting holding a solid block below the surface of a liquid
as in shown in the figure is T when the system is at rest
![](data:image/png;base64,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)
Then what will be the tension in the string if the system has upward acceleration a ?
The correct answer is: ![](data:image/png;base64,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)
Related Questions to study
Physics
A metal cylinder of mass m and radius R1 moves down vertically in a pipe of radius R2 as shown
is very small. There is a liquid between the cylinder and pipe whose coefficient of viscosity is
. If the cylinder moves down with a constant velocity v, the value of
is (length of the cylinder = L).
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58fAJx/XoEbtyIQYBfMM76hyAo8DJO+QTA1/cc/P2CcPqUv/gU/f38UVRUJIoKY7tWmw1WCZAq1ZsKT3FpHaZOX4yMrFKYHDbYxUAF7iQk47mf/xaLlq5FUkoO9h/0xo9+9AusWrVJbMjd7xzCb19+FV/5x6/hueeexwsv/ByvvTEREydPw5Hjp3AnIQ2HjnjjC1/8KiZM+IDcq6ikRuBRUFSBBYtWoqGxCSaLA/nFZWhoaUNPrwk5ucUoKCwVbVNgRw6kTZLHQRYVDAYMNS8mZdHbvXjRMjAuZQwo9PYNwD8gCOeCLqGzq1eOazcZZR4p78DBo2hsagb5Ps8jn9bnkOK6ey2IiIrHlu17MHPWYkyd+jbmzl0CaplsZMsWMz0PKm7F71QsdON3t3wVaqKm6JS4FKldy5FjJ/yxZ/9JeS/KwCGbcqV5n/LDL371O7z8u4n4xF99AV//5jMIDg41lBcHbkfEIOzGTRw4eBi+vn7YsmUbJk2fi69/+xl863s/wnef+TE++Vd/jU986rP40w/+Bf7Hn34UP/jRc4iMTURJZT2OePviTMB5DJosaOvpQ9TdePT2DyEzqwBFxeUiS/k21DiJLBKINkXGVTD48mwGUcmejlp6vhm+0MamBhcVDK/jPrJRFrBpY5NAvHgpGFu37kRefiF2796Hyup6dX8iwrBd5ACA8vIaXA4OxZkzZwVZVCKsVv2kh/sE+ZIMHpL9WZg6YNyUV2/beQB7DxzH4BD9lQDdhVQvSIELl6zEqjVbZBC+vXg1fj9xhoRQeLlhYejuufeDZhsq6pqRX1yBuPgULFmxAX/+v/4Sf/6xT+GDf/EpTJgwAV/95r8ir7gKV29EIiOvCIXlVRi0WJGckYW+/kFUVTeisqoOdjEL6CFRHowH2CBfbPTNUD0Nf55G2NCQCZs3bccpHz9xq+heky+TOsh3r169gYDAC2huUequBrHVZkd0dCyOeflg9pwFaG1Tqj+BpZFF5GoE894CUPGGqLuwr2LLGB3ibrSN99P31H08F3QBEyfPEgWFx/Q5ZIO5BcWYMn0+roZGiX10/UYMnv/FSyJrh4aYnkDVHjBZDCRbaAsBJGzeR7eQ65H42rf+DR/80Mfw5a9+D8vXbEX4rWgUlFbj0DEfdPcN4F5yOjp7+9HZP4Cy8lo0NLYjL79Y3GI0HxiR1pSlnQV8yYeq7uwMAUHtiZ0lK2TkeNPGbeKNiIyMQ2paloxednbAEJ78fONmJE76+KG+QanAZFfatZSdU4B58xeJlshzpXNGJ2kc28TzQNVbGbsarJKYwkwoeiXonSU/93Dwsr964+CRjQB1uBB+MwKv/36SeFo0YIn+rj6TICE45AZ++tyvUVPbKCy8qqYBv3n5dZSVV8NsNqIGYjwrrY+jnzCxGQgj0gaGrLgbn449+4/jlO9FJCal60ehqLQa+w+fAONhZVV1aGhph8lqxa3bMahvaENufrHbVmU6ATVBtsdig8opS1mgKJDyY/Wq9Th8yAvV1Q24eu0GLl66aiTRAEMmpe0QMeE3I0VFJ0scMtEmUZrOwIAZm7fsQGu78hXq5BPZi4GqvBPsKJmUy8XsKnow6DG3Ak4iS23awtdI0nuhdF7tcMno/d2rb+Jfvv/v2LFrHw4cPo4Dh7zwu9cno7K+HT0DNmzYvAs/ee4/0W8Y8IwGTJ81Dz6nAhTQRJZQabKhuYVhDzV4eb7FrpBGhYoqe0+/Utt5IeWkyeJCWkY+Tvj4S+Cyb9CK/MISDA6ZEJ+QJgFOapnkSmyS+yHmxmPKLE9k8UYM1S98eykC/IOE6gYGByXOc8b3rDtMQkBx1FI5iYiMxb79h1Ff3ygd4b+enl4sXLhUPBz8rqhAZRUNA18b4nbx7zlogOo4h8RAbHDaVb6H5zUaWWRZHJvtHT04ccIXS5euxb8+82N87Zv/ghd++bJs3//BTxF1JwXHTp4VFvi9f/0PFFHpcdDIt+HIcR/854svobS0TJBjtloRFRONX//mRXR1dYn4oEeDnIG/0aimx2iY7SvPPblTZlYhVq/ejLr6VvEdRkTGicOgo7NPotKkYL4HZS0HNb0g4ox+HG1QyQOyP0UxAwP9mDplBo57qcAhf2dqma/fWXExuTU3AkvkiQsJiSlYv2ELqqqUGstEmY2btqKzSykhI5F1nww1Ei7dUUbVIbgcRJZKHB0LWbwvbToirL1jALV1bSivakRufili7iQL4PKLK3ElLAq+/uexcvUGnDzlh94BM8w2B4pLK7Bk6XIsW75C3pFIyC3Iw3/+5tfo6OgQn6TVYVFJoIa/UGSO4UvVmi5jZxmZBdi5Yz8SEjPAMA25UkVFHagDBF8ORWlZlbB02qa8h9s/6Ims+wBzn7Kh5JWiLDoklZeAhh5trMCz52VkmY3jHAWXQ66L+t7WrhQH8nS+IEfp7YhoHDh4DFlZueJl2LZ9lxtZmgpICcSFmzoMmSkkyRvxBHIKuiHVSBgl8cRQOIQFudDXPyQj2EbXD2NHShS4lQJ+7TcNe0D4GMofxZBI9Q7UNzaIK4n9qK6rxosvvYjOTvWOTqcZLtAw5j2UqHB7UYw+Dw3akJlRgFs3YxEVGY+21l5YLTZJL6B2ffdeCqprGgRJtE/ZJ42sx1IwdEieACQgu7uJrAW4dDFEvOd8gSGz4tF058TE3hEvclRUlCCTv9OtwpaTm4+o6FjcuBGOnTv3oLtHWfjKFUWWoaPBD+4ZRHQ5XO48QT3I6HmQzR0GH75Wn0OESQiFic68h9a4OIINOSpIou+TkWqxb9Sex9noECYFt7a1YvKUSejq6pTjTJ12uujSUr/zmTyP18lG88BiQ1xcIuJiE1FaUiGJONSMyyvqUFRYisLCclRV18t1vKkkmI6ws8b1uqsRrrrLTjAK2tLSjklvTUVQ0CUJeYSH38DQ0IA7FsOHdXd34+LFi7h06RJaW5X6ToToxmSaFctXuyPL97Ox4fjQf9dxgu3d3ovvrUwF5VVgktDLL7+Mzk6FLK2tjby/Yu3qjcmKr12/hbS0HPGd5hWVobSiVgZxxO045OYUo7KiVmJhvMJt2HMAGmyQ9x9XdSeQeTERR7dTU2ObyCx63Jl65uXlhevXr7tTpEm+bBSQN27cgK+vvwTyFFkzO9aJuroGnDh+SqiU54580ffTdyJLvxP7WlpaioULF0rmlvTdA5ie/dbIIkujokVHsJ9/kCCITu7LV8LF2GdMKy0tFw0NLWIKKDGg2KnAzOP+4yKLqi9ZIRFFhJWVVWHim1MQn5DMvgoimDDD5E7aYGxKk1G5D/fuJeDEiZNobGwShPJ3hveZ1NlteDk8X/L99plUpT01/JyQkIAVK1aIscx38Rz5nn3XyOI5tNPi7iRh3fotqKiuF3fb3YQ0cQx3dw0iJjpeMqkYj5N7Gm4zPs/z/uMii5gmwrTMysrKw+uvvYn4e0kiw3hzqvOkojt37kiOu+ogZ5goaV5YWAwfH1/U1Sn3EtPTNm/aJohWnfvvZ32egHsvnwkwbmx0XDOlYdOmTWhoaFCeH9FWaZzf/w6eyOLgZY4h7dGLIaEy+BnDSkjKlBSIm+FRqKwcTpHQMJH941CWJkvpLYD09GxMmTwDGRlMq1L2ACmKJMusp3PngiSgx/PJPskC2AoLS3DkyAlUVdWht3cQJ477uHM1Rr7o++m7ZoMyyp1OSWwpKSmRASqzYzyA6dlvjSyq73SE37wVg4SkDITejEZ1XZMYxyFXw9HXO4DUlCw01DcL8nkPxc3UtKrHpKxhBYNAT0hIEQWDSPNsSgGxIC7uDnx8GHDslZ+ZasxG2ZeSkg6fk77w9j4jvkW+rPrt/lHp+dL/rz9rZGl1XDps/CPFMKtWADoGZRFpFqsNoWERogU2NrfhatgtkVfZuSWormpCQX4Z2tu7hTppp3KQq20EG9Rk/uCeigXZn7Kx2Gl+jo29h3nzFiIvrxCxMXFu4cvrKdvYkpKSZNJBd7dCGP2CZKNsuTl5mDZ1Nvz9zsFmnP/gs4cnu70fflOjXbE6chDdJ8KEyJLNYJf6N6Y26Hz4wSGLUFZensq9iL2bhLaOHvB4RkYe8vNK0dVlzMoRz4XiWCPv/0gyS7Mydjo09CZmzpiDgoISXL58DQkJSW6FgmlYRChZZ3x8MphKzIxVNqr92rCOi03ASW9ft0Ly/5p63tPzx2GDfHf6Sy+HhCE9Iw9mmwttnf1ITMkSuFVV1ovq3tMzIHBTYsdIT6DJ4XH/h+QNKiOY1MUbsJE0r14Nw7SpM9HW1oXOzl6ZFcKZIcyzY+O5+vzUlAxJkWbWLi1EIpKIv3snGdFR98SKV9coVZUj6Ynb9FS8EX0nIzGYiXAf2lmnzwSib9AiEfQbt2JgMttkMkVYaITAk9yH8OYmarsY1yq9jnAZl7K0I1cji9RE32CX4dejJkhb6nzQRXQaYXvBmoG4tLRMbNywDeVlFXLYbHKIJc8Omk06B/79K7PGpTqPke95rlYwOM7pqWdykK9fEFIzc4WisnNL0drej57uQfic9ENjY6sGm4gM3utd2FkqwZNYJ5s7H3QJE9+YjLo6Facij6ZQDAu7iZ079qK1tV0eSjnFjSPi7p1EHNh/VBy5pM6Qy2GSmWoxG6HrEcLZ86Xf958fAVnUls/4BqKgsBzBV2+gf2AI9LbHJ2ZI3uKVkFDhUgSc5kyEm7y7x/0naIH44F6TI0e9/mwXB+70abPQ0aGmnHJ6DxszTy9evIx9+w7JRDkeU35F+RnFhaXYvm0PKsqrQRcL04glqCf3fn8pFA/C4iH9exQFY9CEs4GX0NjUgaKyauQXlWPIZMKNm9Ho6OhFRnoeurr6DfZHiqLJwyzf+xWYcWUWEaUNYt7A5+QZzJgx223Vq9kZpCLFoSnTOEGNPkThv1QQyQtcENX9uNcprFyxDrU1LbBZndKhJ05OecqncWQWXaJMcg06H4Ka2iYMmW0IuRaO/kELGpo6UVhQIdogVXelNSutm7BWadoeMsuD7jxp0H2YQCbrYqNycPq0P6ZMmYEDB4/g6rUwMe4U7ShvMT/HJyRi9549qK1TOeJaQ+Rv+fkFWPD2QpSVlevLnjylwgNZqjqGCpTeP+gMcIIxNTMCzjJnvkFESVpmHsqqGXZxIisjH9lZhWD03HCUCFworxhX1yES3nuCIc3uDyKJDFGHSB1CXcYsCyZ0zpg5B/EJKQgNu4WAwLPoH1DZqww9MFrK3AlGVPfu34es7CwpR8DxwT+Hw47TvmdQUFQgPNnNm59QueWuPDOi/xIQM4JiFAdXroZL1heVjc6eAVy6Fi5ILC+rQfiNKHR0cL6WUru1fiDRAk+ZNS6yJMFTEQE9Dpu3bMf8BYslG5cPCLpwEf5nA9FleCwY6eQjKRyvh4XB64Q3Kqqq3FQ0ODSEE94+aGhqlkR8yof3vRIxAhGe/R0PWQQ8g6/eJ32xddtudPf1w+pw4HZMPOqaO9HZ2Q/vE2dQX9/spiylvitM32dnjYcsQp5yiY2I2LP3IObOWyh55/rY5StXERh0XhBARDF4xxHElpdfgCvXQpGZnSNINFksOBt4Dtm5eRIE/EOgLE42PHzkONLScxAXnyzBxbqWLkTExkvkgS647i5lpxJmFDuEiwzkx6EsAl/CI+S9ZjNWrV6HKVNnoKNzuAAJH3Ax+LJQTG09ebEDA4ND7gkBNbW1OHTkKNIzqQGacczrOCqqVILIU40swyru6uqV1PLevj6ER8RIVlffoBlht2PB3zip0DSkwkuENSmL7QE7S44+wj9ezkym6TNmCxtkjIf3pP+LGg9D0bcjIuHtcwpEGM/n7A3Jr7M7UFJahv0HDyE9Mwtex70ljZoy7klvShKP8h705BipEEwzZ+pdT28/Glo6ERoeBdPQEApKqsWRy3gWJ0soWaXsWg5ipiK4VWkAE8YDlpCkcRKzkmbNnoctW3fJrAodqddAJ0XFJyTh4OEjwhJ5mUzttHNOkxOlZeU4dPgoVnLUPrwAACAASURBVKxcjY4OncMwXg/e378/DFkcsRyPnLC3ZetOSd6x2l24dCUMXX1DktSZk12EtNQc0QaJLN1IVapxIKjBMK42KBg2Tmfwbdny1di2fbdk23KyARHIxtsxkZONSfacUdLU3C7H+ZuFqasMi5eVY9r0WTJ5gd89hfWT+Hk8BYPvyGImR456IyMzT5BX19iOlKx80QVKiipxLvASWB5JeS9UlIOwEPg8jsxSmomahMYct9VrNmDrtl0SRDx/IUTUUU5qY9N5cpyxkZGZg737Drnn4+pB09rWKaOM4RMi8UlEkGefHwVZlEd79x0WLwZ9rZzyc+1GJDp7TaipbsIJr1Og1534IcKU54feixHxLAOd9xnEPMaLeLGnI5f1lmbOniczQUimrOVwMfiqzA/Wk6Qpw8wWVXeClWSOHD3hno5KttnfPyjTV6n287vizU+gt90wjMcyisXlbozQIZkYf1jmKOcWlIiSlZCajYbWHnR39eOUj79EzwlzpQkquCjD+DE8GLwBGw1jzgqZNmM2Tvr4unPaCXBO+Pb1C0RVtcq45SWccslWVlYp+e5EHBuzd/fuOyjTavj9DwFZ1ALXrN2I1vZ2BF26KuKiu28Id5PSwd9CQkLdsT1tJrlh4+HOmvAwyiKiFIWRJF1oaWsX78Wp034S5Rw0WSVkzRsnJqUJS9Qp0lRBKUzZGhqbcfDQMcTHJ0qnmI3LzF5JuJRU46ebslhwbMnSlZKbkpSajcpazn40I+T6TWF/9+4mu32tns5vpS94UhZ53SibPkQ2yM9snd3deO31N3HihI8R2lZTUfkbkZOalo0dO/fJxDBm4ZLquNEjz+KQRBins+7bf0QoTDmJn+BYFpNbdKHjEV4Oups4CYawY1VTuukYGukfsiD0ZhTaugdQWlmPkuIqpKcxpVxpf/S/Uk9QLHGkzNJYGbEf/mp43QEh2enTZ+NS8FVkZOa6nbhULLiRjnJyi3D4yAkUlygXE50fRCQbK4S9s/egVBRzT2AY8ZKewvtJ+PwwZAnCqLr39YudRXuLAzTsVjS6+ixgsieDsCxiqSeGkw0SYaQq+lHvczeNDZBhgiN1sTGTdtbMubgcfA3Xrt3AmdP+7ogxkWsyYls1NQ0ySTwzkyNGuU6odLDV1jZix/Z30NPTb7DYJ5uyRsLPzaUIMgU29Pf2Y+vW7TLrk0hobulAYmoGhsxW5OaV4OjRk+7J9CytILn4RgKORhbvO248izcfGFCukNKSMrz80itIS1PJHlFRMbhwIRi1NToUQipyyShhqVUvr5NISkwTNiiYkmpgvThy2Av0l2l5KLzZI+zwJH+Xl5IXo1am3ppK1aZNm3Hy5CnJIWQ9qFN+AVLkpa6+Bce8Tol7jmdbmHRkRIn5XYdIeN+HIosnk3/SvmKjPcVJCSzpoxtrMLHUQmGRqupJCmNf2RobW6Sc6s2bkfp0CQUc2H/Ynef+JCNmtL57IkvPfOnr78PKlauRk5OLhMRUmetWXlWLtKxc9PYP4uq1m25tkE5wgo9OXLb7kDWSjIe/K3Vdp4/xwqSkFEyeNA0pKRmCRC0UU5IzpMhwUVGJeoBho/FLeXm11LaNjbkjv7W2dmLH9t1u1X34eU8HO/Rkg5yiRIR1dXZh2bLlaG9vlwmHJrMdnOUfeP6S5MxHRd8VEUIkkRiplGlk3ccGxwYWL1BGsdb9s7Jy8OYbk5CamimAV8JQjYDsrHwpNMwq02xaQeHnpqYWqRx9/doNQR4rS1PoqvOeDiRpOLpf3ENmUXXftm27zDypq29GVnaelKMtq6hGW1s3omPuSfhJKEo7xw2T5pGRRYCzKVXShbt372Him5PF1USvO+WTDvkTscVFJYIwnVpNytP3aGvrlARRzvSngkI5qBD6lCPLCXS2dWLDhk1irlDTYz0rihZO3CsqrkRsXKK7koE7hW1EdhOB9VCZpRQAxQ7Jn4ksJniyvLev71lRxRU6h/83NjaLlpienuU+qBHGXASWv+P1RDbvPxrff5KPecosrWC0Nbdh1ao1yM8vFNW9sKhUZutz0jjLkV+9Gq6q3TCqTAXDgJzAQZcVH0/BUMhS2gIvpPZHNlhSUoHc3EKpx15To9KjyRJZvpuNmiBLL3ASg+fEBP5WWkov8wUpisjvTzJiRuv7aMjq6+nD8mUr4O9/VpQH2lfnLgTLDH/WjGe9EGqMbEPGBHB+pp31GAqGAqbyNLgQHn4Lr736hqjdvBnz3Q8fOo7MDKryzK1TyTXct7d34eDBYwgOviqhax7jhPDi4jLcvh0tDl3eQ/P6p2X/gMxycV7XEHbs2AVW4+Y8rIFBM+LuJqKnr19K8l2iv9DQuMkGqWDIDBWPyXTCBscGklISlLtJ5QOwyvSc2Qs8gG9HRma2FCtOTVXVVFQWLtEASfZkjfPDh4+7BxwpMi4uXni0otynXGaxGkB/P3bv3iPZyvSrco5xb18/Yu7EizHMQv6cw0UkkY8xcqHExPDEhEeUWYoNUpUMDg7BrFlzpXSoTpsiUiorq7B3z0HExd51Kxz0XLAxY5fejksXL4uxTO9GZGSsdI6/j8ZKnuRj7lEpOrgYSjLxbu/e/VJT+F58EnJyCiSf5fLVULS0diIvv1QGLx3fWsHQkeL72ODYgBFYCzBJxtRiAgIC8V8vv+qeKEfWRictW21tHc6c4WIySnX3lHccSczUPXM6QGaVUJYp7/KT620fC24PIIscpqsH27btECpirsX5C8GSz1JZU4e0jDypg8F0NSKKpKHIQ4mIR0aWZlNUz4kszhaZNm2m+PdYzJjqOjU91XHICj4sOp+eli3lUJXqrtR7GtdXQq5jyuTpSEpKE/lmNg3Xjhjr5Z+046Mhq7ujC4sWLpYSQoQZvRj0YDBdjwVLOIWVMyvZhA1KKhphO7wMIu/70Ck/pBxdBog8dM+efVIU8vbtKOzffxipqRnyAFIXz2WjZ5maYFQUZ++raais7kmkDg4MYvu2XcjKzjdsNzV6xpabT548k5LhNGgZIlGF29Db04c5c+bh9m3ldmP10tDw21IzvrikEtdDb0t8kPBj7SZWoeYgpejR02BFZsmBEVMs1TGerKiCNyGyKCRZG5eJMwUFxVLYODVVUQnPZTCROGtpbcehw8cRFnZbKnzyeqKSXvlr18ORX1AiE8p4fOznP2Tmxqj9fb+dr+DHQcoFClj1k6o7BzCVttiYu6IRcyD7B5xHb59KPBoyW8TWIrKYY6mnwbocjodTFh+kWKBa1OTw4aPCxjiBjo3LHG3fscdNYUSYxVAs1NTM6wg8d9Fd9of1CC9eCgHrDbLmE/k3kfU0UdbwuygRQRgyjsdJ8Xl5BUhIYFTYKkVKGL1gdljYjQj09ik7iyVXaRhryrrP3TS2TKAsUsiiwUss79r5jpTx0YWMaX9VVVXj1OkA3LwVLbMiiMQ+Y5T09Q/g1u1oSR2mdsONtd7pG+NzlUwbbQbG06B4KPgRHvTq7Nt3QGQWp0PR1UbxcuUK1xjrkyKS/K5Vdx0iIeIfS8EQEjISXdav3yj1cckSOWK4sdE5yXqDoWG3pYw2kavLhbNMKWeceJ88JSEWhvZZVIpskZePPViedIRpyDHyUAmq7nReFxWVSYiJ7JALAzCelZKaJao7RYjAxIALuc59yBom25HCXJOxklt0h9AZyfq4JGM2Uh6TN/kAGnkcKawqreuZ64QZrqiQkpopkxoWLlomkVKOIuZpkM2O3Ycn+TcFP4oGVtZ55529YnOKCeQfJDnu4tEpqUJMbIJog4SjVt8JX3Ki+9jg2IDSyFIjhO6QrVu2y8KZ9+4lgyF7QZhY3Ooc2gpxdxIkKYY5hmy0xnWBYvLoRYuXo7SsUn7TpsHYfXg6kMV51suWrXA7vvPzi2S1CYqBisp6qZg2ZGjORBZh5pblRkauaINjA0r5+QhQbkTWmjXrRBsMDDwviZ5RkXEyWsjSSEUcGVw9QDwWwdfQ2sbSpMrXRezQuF63frM7b4Pp1u5OPeGJMw/CUSUakXOw5OzGjZvdqntv76Cs40IljBPBL10ORU+v0gYJQ+ZhEC7UoTVlSb3BsWWGkid0F1GRYAWzxYuXYv26zcK2mB+4c+deWSBGSoWKjcD8QpXzHhd3D2fPnndXnyayuPwQM3QZjGTGEzVCCtOx+/Ak/ybMQ5wJTDS6fPkKIiNjxMFNimK0va2tXYKOkZF33HYWBz6pi40D4LFklrasuSD05MlTsW/vIfEI82acCXI28KJog6y8zEaWp3PeIyJjpIZ7TY2qhsY5W8x/LywqF5tMa4MPjsonmf3pviuORM7CdIeLF4NFwbp+/YbAj5zq7t0E8Rsy35LriBFuWiPUA1hT1jhsUMkshWGXrO04f/7bsrgzH6QznpilRKPu9JkAdzoV8dY/YJJRlZdfJNMzOaOEbn9SFgsMs3FFoKcTUXwvBT+q5MXFpWJnsQpPdHQc6Mym8pCcnIbm5g6ZEcmMJyprWsEgXAT2jyazaGPRUctJXi5x8y9ZskxW56ZqziZs1fCsX78ejkOHvYS0+RvZnCbn3LwiKReemZWHjawz2K+Mao6ipxlZpCrCihHi06d9xQtEI5gOb07QYPXOgsIKD0euymwimjgRkZPpHoOyFLKobtJGIGWxXCqjw3RCEvlaPe8fNCM65g527tqL+nrF9qiyk7S5VVTUSLlwzkdmh0WQGgupPZ0IG2aDaWkZ2L59pwqDWO0ICbkuJesYWU9ITMdFTlM1SrFzTgG1wVEpS/PGkXshQScTPJWW0tLShoULF0uIg8urM+mFI4eNiR8EPqmJQpQURtJnI6LoM2QjZW3YwIVZVGYTj4587tPzXV5ZBjSzwtasXouS4jIJKbW3dYmCQVOH6eaU+1qsEJZEFtsDRvHYwFEjgxeRDVL9nDp1htQJpJw6HxQsORhdugozqcyY3ZiSmo4DB71QXqby3UmBfDxJf82a9e5iwFyaaeznP8maIPuukeUE0/N8/QIQGhYOlghnKjkDsFTdu7r7cTuCwVhVVomDnmOblCVmjUt5MXjDh4ZIlJBUQKP6uWjRElwIuiT6P2UZKSwwMNBdvo42hZZjxUVlCDoXIsafYMooZLxt20709/dJR54GG8utSShgKa1CbEaFLCoSnOoUeiMc1bX1MrGQ0QcuwcRFargaOheYEd3AcMFpZAmhPJ6CoepZcAXvSZOm4GZ4hJufkufGxsbC29tbAo+KCpViws/5eSVSnu3OnQTpOQv4Hz/uLbXeOXJIVU+6vBoPWZT3zAq7HsZqaAPijuvo5EI6ZkRGxcrk8KRklYNBYiRlyaadBI+KLA4WrflxFdA33piI0NBw0RIZqmfjyImMjBQksM67bmaTXUoL5GQXYP36rTKZobOzC2vXrpdS4VarRfHkJxxhD0MWWeHQoFmWsr9zL14WTssvKJYV7ljWjtOm6MiNir43KhuUgeyJrLFlxrDM4kObm1swd+58qZFLGcamWR7vkZ6eKfXbmYvBxhIOXIyHraqyDnv3HMKpU77w8vKW1GFew7CLprCx+/H+ll0inAigERu/sjnsDqSmZeDcufMyOElpXLOFNUVoi2bnFCEkJEzcdjyfl5ENuuHxOEme+qHku9OmzcCFC5dVdg7jLxKcVMFDRj9LSsqkalp1tZoCRIQ5jKmqra0dsv6It7fP8CgyWKG7Y0+g62kkkvR3DTcOxsjIaGzfsVOWoKLhW15RK85sen04P+vK1RtuZGkFgzBRyFMuJ9533PRpXkPhR1th+vSZuBx8FbGx8eK1YL4FGzUZjhieW1paAX//QFBdZbNaWOxQPZgr/LCeLsMtTzKCPPuukTNyr5FFr82tWxG4ej0UAYHnJLWB8oqhJGqDLBgZG2eESJjcyZCRQG4U1X1sAa8UG2p4XOEgOztX2CAnHdC5yyk8ZwPOu9N+2Tn6+tiYn3Hi+BkpBsnv9IQwdlNdUw8ud0F/I1+CLz32858MVxRzI0bb+M5qoFtw48ZNWeHo0uUQmVvNYpGxcfGg7cqV7BIS09QsEiM8Yjc4zruIZ7FKp0MeOGfOfLBAsW7MYDp//jxaWlrkkCZdfqmsqMM7uw8i4naMzFHiMSLxxo1bYq0TSX8Iqjvl8oULl5CVk4ue3l7JGSSy+vpNiIq+IwlF1AZNuvSfkeFERHvOKabMGZcNEsgEbFhYuKRTcXkKKhbMyKWikZmZiXPnzkllTj2aeA0fVlpShbP+FxEj2o5VkEXvM19AU5UnS3kSPz9MGyQciJgrV66hpKxcUszu3E1AbW2DqO7XQ2+irb0X+QWlYiyLfWUoGIQ5Keu+EMnYAFJsUByyDpewL0Y7q421hbUvix1iOtr+/QdQVKRcTERUrxFMa2vtxrmzlxAREYuwUK4GdFfYKBGmkPr+1vbGho/q90hZpb8TBmyU95wjkJyaJm4kllegNki5zSXaqWCkpbN8ONeOVNogLyWy5NmPow3ygcQwKYKRYk471euMsEO8IRuznI4e9RJFhAiW64zV+cxmh8zJWrZ0FeLjk2S08TLxfT2BGqAnAjVyRu41sogEIuvgoSNgFVMuaRETe0/yB+m9uB0RJ5lhOn1aaYPK+04YPjJl6QcSWUxQ1KnTgYEX0d7RKWyQHdflwktKSrF37yFxUvJBLOZJ1Z0Zu5wMzoWoaQIQSWwcXU86wsZjg0wbv3UrUopjxt65K2tntbX3oKS0Supg5OQWy9paRBYbIaNXVH2ADZLcRt8UGyTCODoCA89hyZKlUss1NuaeUAqLRLHJTQ2y51IW/v7ncOtmJJyka8a7jFyL6Og7yMzMllABj1MrfNKVjNE0QR6j/GZjKsOJ495SFPPESR+Z7mOy2EB5xSBsZ9cAklIyYbMpjxBVd268mnC9P57F8IZMgjOQ5uIJau1dPc2fs8v9/S9i7dqt4CJd7EhCUhL8As/KUrDsFEcEC/Wy1dY34ejx07gQfMWdAtDTNwBOcWFtXKnw6XKAi0iPPlCe/OMMDbHRrXTGzx+FxSVIy8hEXiFTx21Iz8xBZk4+BgcsyOSCMmaaMgwpuaRsrY5IaGSpBTo5E0Rmg2hkMYmF00/UIs+8AdOc39l9FAsXrkGfEd9iRzJzs+Dl442s3Bw5f5C52bSdALR29MpSDgePeEmeAe21W5ExSEpLxwDPY9lwruo2JmU/2b8ZhCUZXaxeWlNXL6skBJy7IPKqq3cA18Nvo76+VSp5mkwKWYQriYFwYdPI4vcJgqgxkEXjjCo6Nb89e7wwfdoCdPcOyHryBtdDXlEBTvn7Ijouzu3Xon7BR3EJh5On/XDyTICE+znTLyElDRa7HVYuC0Hx+ZQjiz5AKhf1jU2SyZWdW4CsnDyZQZKSkYWsrELE3+N8NYUsoa77OJ1RbGs8ZJG62PoHzDhxIgDLlq5312eyG5TH32vqanHg8BFExcTK+bxK8gjFq2HFGf8g+Aacw76DR1BQXCJs0MK0gD8AZNEVx7r3585fkOLOXKXO92yQlGLtGxxCbEyCLC5NZA2HxNQgFnlueN0fgbKYs85Z+Fbs3HkQ06cvQGFJOWrq1Qo/FocNZpuKcNI6P3DoMCKjYgRh/McZJdIBF8Ran79gEcorqzBoMsso47r0zqc0fVqzQWYtnfH1w959B8AQEUP2iSnpSErNEOpircFbN9VkOsKKlMVNt8dgg5zq45A8jLlzl2LVqi3Izi/BsZNnkJKWJvdjBq4A3eWSHHefU364HHJV5b8JZTklp723d0Bq7hUWlUjtV/aHBfmfdG1wLDaukUUFwy/gLDKysnE7IkoGaf/gEPwCz4NKV3VVo8gsaty6aZnlqQ2OS1maDXLGw9q127By5SZxOBYVl2Ll2jXIzFGLdHLtEZmtZ8x8ZOVpVkTr61deCi6QwtRpVmBm6VYiiizwqdYGDergXDYqGG0dnbgVEYnCklKhqNvRsaiorkNLc5csHKMc24qqNLJkIHiyQYol2QwPuMPJPEFDnhjBMBqvCxeuwrJl690GcHllJc4E+CH2Tpzkt1NOMUebjS6V4JBQWTavoVFFj/sHBvHOngNobG5VqVZ/KMgaHBQW2NzaJsU1r924hd4BEzq6+xARfQdNjR2yfpZ2zxF+1JyJKDoc7mODdvEyDLuNaDG5xM5yiCVN/skQyZYte7Bvn5fUyNMstbOrC/5nAxAdGyNyiA+SBczE4KWb5Ra8vf1AhDFJhLVxu7p7RdCSfZIix2IjT/pxzQY50Ll4TnVtnSxEcDchBc1tXWB9Ycqu3NwSoSyq7mxayRBEUVP2pCxP1Z0nkLLMlkF093ajpa0NLNzf3TOAjRt3Ydu2/egzCkVa7aQ+zuprhJ+fn/gOyepIwky3Iq+TkHZKJoKCglFUWII9ew54+BWVI/RJR8pY/dfIoj9w1+49iLt7T5DR3tmDmLsJohFX1TbIUu15OcVCTfQpaL+q4MKjwgyfM4FAJcIozCjs7Q6LIKurpwstrSpO1dnVi0mT5mDr1r0Sf+H6IgOmQTFq2QMmbfr6+uH8+YuSGygTDoyyC4wS37uXAt8zZ7Fo4TL3shYUvGO96NNwfBhZJqxbvxGHjxwTEcJlPuLuJaK1vQO9A4MKWbklgizP6jzKhTeCDao8iWFkKccRp/STDapQfWVlI+bMWYqDB08i7GY0ouLUKKGSQHZG4LKFht4QpPT3DcJqAchinYaSw5pNLCXE2ntstD84etzk/pQZx8PIGsKOnbtxMTgEtyOjhCC6e/pw/tIVDA4NoiC/VFYAZ4DX8NaJ6k5kic/dkw2Ssogw92h2aXeT0tYon1gr8PdvTIeXlx8KCotx8OhxXLwcDBuxYThkuSfObt2KklxBCk7drBaHTMbbumWn2Br00lMWUgN62lV35qns3LUbNXV1OHz0GPr6B4WL+Z87j9b2TlneoqiwQqLxhAnFCJt7EHsiSwwxd5UYJbMot5RvUE2OY27b1Gnz4ed3UW5U19ACv3NncSGYSR+qJAAfQn7LByYnp4MLcVZVqQkKDJNQnvn4+KKnu0869jR43N0DfBSuoCmLqjszm7g6X1FJCRKS0zFgsqCkvBJFpZWoqmpAcVElHMaqPgypEIZsEuOiEkaEibtplAd5doJqJCcwL1q0GGfPBsqo4I24zuPly5cRfOkC+rn6N91P7tx1ICszGwcPHJbJCDyftpr3KV9QhTdZncr1YlNJ+FZOLbK7wHldfEn67pkQZXU4ZU9fo5WpBJStTDw1zuF5rKtudynNUuw2I1zHz2TjMj9XpsqS/5NbcACq4ipk3nQnO1w2WB1W2RyMBsgx9pG/GedzZofYh8rvyX5y5pPYi3CCnk67RBKMZ5DFS+3FXixfvUZ8o+Qkx06eFmc4zZwroTdRWlom8KUMZ9PchpSlPxOu3B6S6670fN6gqqoKc+bMwc2bN4U8eSEb5U5sdBTO+HhDJii4nO6cQD4sOzsHK1etlyIlfPCKVevdVZblBk/hP408QTJc6OzpxeFj3igsLhclgu66iOi7YhhnZufJgK+oqHAPdIKEsNMI8iScR0JWWVkZZs+ejYSEBLcy4ca63SHUdeTIESnKwYeRxenIJ3M2uLRD+M3b2LRlJ0rLKtDc0g4uzdTY1ILaunrZGELgwjP0HXKNrZJSbmWy3GBpeYXEg7h+JONhWdk5SMvKQXJ6JlJS0pCali4ZwRkZWZJWwJwQHmOuI+sgctGa+IRk3L2XhITEFCSnpMqxpORUofz8gkIpdV5UVIzCwiIUFBTKBDge5xK9ZWUVsgBORUU1qqvrJOGlvr4JDQ3NaO3oRGd3D3r7ByQP0MLlQDwGIZOX5y5YhuCQG3KUcDvm7Q9W22HAce/evSgsLJTfiCAih81zrxH2UGTxJN68pqYGCxYswIULF5CamirxKfqyrDaunKoY7PXr1+X3zs5OlfTJijJGmnV1TR2mzZyL3736BhYsWollqzbg7cUrMW3WAixYuAQLFi3F/IWLMf/txZg7fyFmzV2AaTNnY8q0mVi4ZBnmzF+IydNm4vU3J+HV30+U7fU338Lrb7yFV159ExMnTceMmfMwa/YCTJk6C29OnIo335yGiROn4803p+OVV9/CSy+9Ltsrr07CG29Mx2uvTcUrr07G67+fgjcnTsNbk2ZiytTZmDJ1jmxvTZqFiRNnYsbMtzFt2nxMmTIPU6fOw8yZi0QznjdnGebOXY4585Zh8dJ1WLthJ7Zs24cduw7hnb3HcOToGZw6HYTAcyFYuWqzHCuvqJGE19KyBqSlF4gcj4qKFPhqBHGgeyKKVKa3hyKLJ1GFLCoqwrx583D69GkkJycLK6OqKZm4dhWO5sMyMjLQ3a0W7qRhTFzxHpyXxbpFoWE3cTXsNq6FReBWZCwio6LFSx8RGY2IqGjcuRsv909JSZHlCGNi45CSmiobn5uUlITk5BSkpKRKRlVaWjoyMrNk/hOngpIScvMK5DvrHnLLyc4DM4EzMrKRmZkjVV1YnJHVXXicVMeScvHxKbJPSU5DakqGKEmJiWlIlN+SERmZgOvXo3Hx4k0EBFzB6VMX4e0dhAMHTuHw4TM4esQP+/Z5Y9u2Q1izZieWL9+CRYvW4fXXpmPFik1SWSYw8Ar6+lizyinKGjXF6upqETOEJZu2dwk3HtNUxf1DkcUTeAFnkOTk5EgReVIab8gRwL0eBbw5mx4Z5NkUoixeotcokROegn98U3IrKhgU30oTVolBXACGSwIyysDV95gjyJW/WfOjtrZZ6lsxTaKopBytbe1gklFtbY1MnicMCU+yQ37W8OUxbuMiSysTnjDmTfTGmxCBNKK1UBw0DYnmRe2LGhW5MKdfmq1MWuTkZmZE8RrFROXlqdlRA6IGyA6TKgkU3oN5CUYiidbuRICLo1PZg+p3h1yrzlFamc3Q4ug5EG1OtDhlkjBPgp4x9oO/qecpJMjaXtQ6jWm2+rsnWwQaAAAADZ9JREFUHJR08Twy9me+E2ODhBNz3NkIN86/1rNpCFONJBIJP2uYcj8usnjBWBsRRWRYrBZRYblUuxQhMV5c4lyCBEMll+mXalRyZMrmoQ4LMEd8F1WeQBttM1RvO+1C0JinAm2D3UU7kXkkNticaiCZrWZmfIj9aHUoW0YcyazOJn5ONXDYZ35nOhibDC4jZscBotRzOlhdMFktqu7HaH2TSDoHgVbrVf+GzIOwOsz0/cDmMAsyNOV4IkZ/1r9x/5D06bGRpJHHG8iLCkXY3aOTSONI5m98QY0Evji5peemf3t3e96b1Eok0U4yweGi0qPScRTiCHibKEJE3JB1CGJLCTBJiUoDY9/YXzMRYNRT53UCbKe6nui02M2wOjg4iUwq6mP9KY+52cI+GX2UvtlgdxLJZgya+gyZ9GAuCmFM+GpYc/+ekCU3NNjXgHlIRiFfmkvkcYSy8XXklR5CoZ4derzPTlgdfC4RZIXNaRLEyah1WmBzWoTSTFZVcYD9ISIsdgKLI9sq300Wk3xXjFK6Lf+sdpMMBlIuM744COwuIsoKu4vXMD1BuedG2zucFpgEIWZYbP0YMvXA5eLSi/1wuGgEW6XWBetdPMp7vzc2SBZCRy4NZIcNfYP9sgoA35QeBE1hzlHyA3XgZrxOerKB0T5b7VyJnJonx7oa6RwowpKlZ5Q7dplyw3pSupktDhH2Qi1WC7p6e9Dd04shi1n8eFxifrhRZpJyLbIJ0pxkt2Sx5CKeG4+pzSlebCeGzAOwWE1wOGyw2RjVGJI1BvmdRYtHe6/Rjr0nZBHQdrJAeoKFv5OugAHTkMgyYZFjJMSoZMXxSyuM1un7jonMITtTck1WHDfmRvE8liifPWe+2Hjf+NZ38NakqUhMShE/JpUL5kHyPZiZ9cwPfojnXvgFlixdjud//gJ++rPncC00VFg6WSfdWmSlwhql5AFdWCMpa3idRioTeu40ZRATZgROLrUmmY4Ia/k02t7zXd8zsuTpBrtjVLSkrATHfbzR2d2lWKD2PRreY40kvX+vlEVbzoh1iuY2OMgBoHpVWFiFGTMWSWZWfHwmjh71xZe//G38+Me/FoOU53F6Lfft7R34wQ9/gk99+m9FnS4uKcHzL/wKz/7HTyQRiLc0bqtfedw9+0Zgs7Fu09IlK1FjrOJH5zbnAngiY7zPExS/HJtn8kG8CbFOwHJOlu4Af+vp7UdxSRm8vE/gtTfexOe/8Hf49F9/Vhy90sv/C/9o75CdUUOjwclG9fjmrTgEBgaLE5nHrFYX1qzdho9//PPi4uIxFiXlnIDunn689PIbePW1yfKu/G3/QS989ev/jPaODqUV2p1iN3J+NCtKM6+faQpMe+jr54TuIWGtOnWa9/Bss2YuwPPPvYjkZJVoxN/GG6yev09wgYKTm1YFjL2hjWjSVEmIw2Orvr5BlqyYPPVtfPkfvoMJE/4Ef/rBj+ODH/4kPvPZL0oudz19Z21daGvvFl8gS4jTL8i65nUNTeDvdXWNqKmuRVlpBXJz8sWfR39felqmzEtOSkyWuWFxsXcQExOH2Ng7SIhPFJ8gfYEmc7/IDJ2roHRPFwZMA2htb3ErOgQM5ei5S+fx8U9+ArkF+fLGVIO43YpKwle++j2E3VYr6PFNN23bhx8++4LUWuT1XCh7+65DeP4X/4Xf/vZ1/PKX/4WfPf9bTJ42H6+8PhVvvDUba9fvxNoNu7Bl234EBIbgfFCQbGHhEfjNS2/in7/z7/ju93+M8NtcilHRq5g7j6CATaBtorZhXqvjJ0QUDTY9w4FlgK5cuYp1azfgJz/+KSZMmIA/+9AnBEEf/Mhf4cN//il89C8/i4/8r0/hH776XXz/336Kf3/2Z3j2x8/hhz/6KZ75wU/w/Weexbe/+wy+8a3v4Zv//D1865vfwde/9m185ctfw2c+9Xl85MMfle2vP/O3+Icvfw0f++gn8cE/+3P88R/9Cf74j/4UH/7QR/H5z/1/+MevfB3f/c4zaGyql1QEpa5ztqCyq9SQo4FNI1SFH5ineNrfH1/56ldBHybPYWXzQbMDh7z88Xdf+iYGjJXLk9Ly8MsXX8OS5RswYKJdBAya7DgbFILFy9ZhzdotWLZ8Hf7rlUmYOHkufv6r3+Enz72IX/7nq3jmh8/h6998Bv/41e8KjCZM+CP82Yc/gR/+6Of40le+hY9/4nP4zGf/XjzxQl1aVIyzn6BH5AN7jwuV24M57ybcvh2BWTPn4Nkf/Qc+/7m/xYQJH8CECR/Chz7yV/jQRz6JD//FJ/GJT/0NvvntZ/Cjn/wCP/j3H+PffvAsnnvhV3j5lTfwxsQpmD33bSxfuRaLlizHzFlzsWTJCinj+s47+7B79z5JrGHeoZ9fIE6ePANv79M45eOLgICzOB90AZcvh+DqlWsIDQ2T0LjmCnwH6SuVGolDURVQ/aaXYtBkwusT30LAufPiPSACyLIGhmxYvmorvvDFb2DJsjWY9/Yy/OznL2HvQW80NbeJTkmriufbaAATwmSrNpY7d2CI88+auxTHqG9CWUUVCotLkZ2Th/BbkbgVES1L3P/dF/8Jn/zMF/DBD31MPPE1Dc1yH84QGU9e8fcJ+kUf2HuQJV0f1Fx04+eGhkacC7qAX//6JXzowx/DB/7kg/jc5/8eH/7zj+NTn/4bCTG0tXWgta0DLa0dwtsHhkzuZFDei3f0uK2+/WPvydfJBbS7Rt1buai4+psA2WbH4SNeWL5qDZhnb2HZVyOckV9YiV/95k0sWLweu/Yexwf+5MM4dPSUeE14L5OFyFfIkj4/dg/VBd/69r/gH/7pG7h0+Zq7soGnTBrv87jI0soF8ybU/GLaBerhVDaY484lmSIiY7Hg7SX4689+Fl/4wpceKchIIOqmvRrD37UHRQlhpdgMX8Hz6UBl//iSVOm4Z9/kqzEY5DdAavn+/o1JqG9SefqMTjNLiz67U34hePanL8qgau004flfvIwLwWFKorCkj4XnqpKopFgijp4ZKx3ZIu2V2cDjEtVmhVLtA7Uofyjjd8tXrAZjZmzMUn5UWaWROK4Hg8CQmxvJLQogSjukqu7ZOIGB01cZ6iByWS5AHLkSVueLKLakQ+58UU0RpApSrO4Yj2vPPj/Lmr+CE7WcLPul2LOBHEEWNVeVC8JZLPQnsnF94GeffR5xdxLlOwHKRsfyoMmCpSu34vcTZ0v0trffgu27DmP9ph2S5MNbkO0RObopxy8dzCx+ST2Uripmg6lZiwqJCrn8XTuidUCWNfAlhPS42iBfeqyNQNLeX3qI9WeeLwAUnyAZqMHPPXgaAcWRo527RJCkrRFBkh+hjEvtWVNeeyLMLp5p3Sf9O00M9zmyVJH6hQCkrUTZoamPe3aFI51L923bvluoRgObSgVnIRLZnb1mvPr6FBw4fErkGN/k3IVrmD13sZSX47vJ5mLeyYCEifju9CEyu4uzOPmeeiAqSlNChc5gHreR+g0YyXmEC6f4GBq3ftfx9uMaxePd4EFvuHL7ECH3bSoN5YH/Dyg2OvXqEfcEHNmzYtFK4BNZUkuqtBxvTZqGufMXSYGvQ4eO4six45i3YBHmL1wquAsMuoqPf+IzuBuvlpfiwazcYoke5+SqcDuJqrGpCUe9vHDypLeweFI9ny1urpHv+hjfx4Ov5+/jskHNloaNZ7Kq4Y2j9/5NGacyaoS/G9/FSUM2eP+f573ezWdF4UquqURJxa6aW9vhc9oXc+e9ja9945/xlx//NCZM+J+Y8McfwN9/6StgtdFlK1fha9/6F3zy01/A7HlLUVXTIFTEQOGy5avxs+d/iZiYOxgy2dDc0ipZtaz3wbQ6NqY2CDA93/MxPw/DV8vosfcTDNmshPJ94YsRFxmi9EGtUcsMvR9xndYqx7x+jPP1dePsZXQbbFkgaPyjbcUEm6LiYuTm5kqmFVMC4hMTkZ6VK0C+HRGJO3fvISk5BekZmaKxUjZxNn11dQ2iY2JQXlEteY5ETEjIVVzgkrXugitqkDwOwN/Luf8HkPWYSBsHGeO+HCNLDHfYVcyJI53ydbymKwt4nke2TY7QP6iMaM/fqDCxiimrkjKXX+elj9u/9/p+Hte/B2SpAN8jU6Z+6EgK08ff5Z5hBheTKzmh3Em25BBk0XNhsppFAeBnApVGsQh9lwvdfX2wOVXwkfOjqbXyPPGUc0kpandcjZvaHpWL/iFcOH8Z0VF3lD1HDZGTZd5lv9/NdROomY++jdASHxD4RmhgzOtH3nfE/dxa6MjzHv077awhwzdoEcQw04oyUoo2GJm6KkwvmiQdvXYrrAx1MHzvtMNkH4LVZYHFxliVFSYrA478o1HNxCBFpdSEA/yDcCM0wr2CrNP66H0dHca8fiy4PHj8MZBFFuG56RzsR+3wgw9XHX3U60c/z1Cs3eXeqKTQRGD8SSv3ZG/i3XCrzw6YjXwRxqiUHFZnyzsSWS4muJBqVZYR5dTpU2dw/RqrbtrEVrHrCe6PPGBHe4ex4PLg8cfQBt+bIvBuyP7/5DWUR+PdX4wjsjuHQ6Yq7d69G4cOHYLFouZKc7CNd4//zt//YJH1OEAkYumlDwgIkLLoWht8FIQ/znPGO/f/R9Y4CgI1S1IQ2SgXJpXQimEq/N+mrP8NI4/CBcQ9QjQAAAAASUVORK5CYII=)
A metal cylinder of mass m and radius R1 moves down vertically in a pipe of radius R2 as shown
is very small. There is a liquid between the cylinder and pipe whose coefficient of viscosity is
. If the cylinder moves down with a constant velocity v, the value of
is (length of the cylinder = L).
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58fAJx/XoEbtyIQYBfMM76hyAo8DJO+QTA1/cc/P2CcPqUv/gU/f38UVRUJIoKY7tWmw1WCZAq1ZsKT3FpHaZOX4yMrFKYHDbYxUAF7iQk47mf/xaLlq5FUkoO9h/0xo9+9AusWrVJbMjd7xzCb19+FV/5x6/hueeexwsv/ByvvTEREydPw5Hjp3AnIQ2HjnjjC1/8KiZM+IDcq6ikRuBRUFSBBYtWoqGxCSaLA/nFZWhoaUNPrwk5ucUoKCwVbVNgRw6kTZLHQRYVDAYMNS8mZdHbvXjRMjAuZQwo9PYNwD8gCOeCLqGzq1eOazcZZR4p78DBo2hsagb5Ps8jn9bnkOK6ey2IiIrHlu17MHPWYkyd+jbmzl0CaplsZMsWMz0PKm7F71QsdON3t3wVaqKm6JS4FKldy5FjJ/yxZ/9JeS/KwCGbcqV5n/LDL371O7z8u4n4xF99AV//5jMIDg41lBcHbkfEIOzGTRw4eBi+vn7YsmUbJk2fi69/+xl863s/wnef+TE++Vd/jU986rP40w/+Bf7Hn34UP/jRc4iMTURJZT2OePviTMB5DJosaOvpQ9TdePT2DyEzqwBFxeUiS/k21DiJLBKINkXGVTD48mwGUcmejlp6vhm+0MamBhcVDK/jPrJRFrBpY5NAvHgpGFu37kRefiF2796Hyup6dX8iwrBd5ACA8vIaXA4OxZkzZwVZVCKsVv2kh/sE+ZIMHpL9WZg6YNyUV2/beQB7DxzH4BD9lQDdhVQvSIELl6zEqjVbZBC+vXg1fj9xhoRQeLlhYejuufeDZhsq6pqRX1yBuPgULFmxAX/+v/4Sf/6xT+GDf/EpTJgwAV/95r8ir7gKV29EIiOvCIXlVRi0WJGckYW+/kFUVTeisqoOdjEL6CFRHowH2CBfbPTNUD0Nf55G2NCQCZs3bccpHz9xq+heky+TOsh3r169gYDAC2huUequBrHVZkd0dCyOeflg9pwFaG1Tqj+BpZFF5GoE894CUPGGqLuwr2LLGB3ibrSN99P31H08F3QBEyfPEgWFx/Q5ZIO5BcWYMn0+roZGiX10/UYMnv/FSyJrh4aYnkDVHjBZDCRbaAsBJGzeR7eQ65H42rf+DR/80Mfw5a9+D8vXbEX4rWgUlFbj0DEfdPcN4F5yOjp7+9HZP4Cy8lo0NLYjL79Y3GI0HxiR1pSlnQV8yYeq7uwMAUHtiZ0lK2TkeNPGbeKNiIyMQ2paloxednbAEJ78fONmJE76+KG+QanAZFfatZSdU4B58xeJlshzpXNGJ2kc28TzQNVbGbsarJKYwkwoeiXonSU/93Dwsr964+CRjQB1uBB+MwKv/36SeFo0YIn+rj6TICE45AZ++tyvUVPbKCy8qqYBv3n5dZSVV8NsNqIGYjwrrY+jnzCxGQgj0gaGrLgbn449+4/jlO9FJCal60ehqLQa+w+fAONhZVV1aGhph8lqxa3bMahvaENufrHbVmU6ATVBtsdig8opS1mgKJDyY/Wq9Th8yAvV1Q24eu0GLl66aiTRAEMmpe0QMeE3I0VFJ0scMtEmUZrOwIAZm7fsQGu78hXq5BPZi4GqvBPsKJmUy8XsKnow6DG3Ak4iS23awtdI0nuhdF7tcMno/d2rb+Jfvv/v2LFrHw4cPo4Dh7zwu9cno7K+HT0DNmzYvAs/ee4/0W8Y8IwGTJ81Dz6nAhTQRJZQabKhuYVhDzV4eb7FrpBGhYoqe0+/Utt5IeWkyeJCWkY+Tvj4S+Cyb9CK/MISDA6ZEJ+QJgFOapnkSmyS+yHmxmPKLE9k8UYM1S98eykC/IOE6gYGByXOc8b3rDtMQkBx1FI5iYiMxb79h1Ff3ygd4b+enl4sXLhUPBz8rqhAZRUNA18b4nbx7zlogOo4h8RAbHDaVb6H5zUaWWRZHJvtHT04ccIXS5euxb8+82N87Zv/ghd++bJs3//BTxF1JwXHTp4VFvi9f/0PFFHpcdDIt+HIcR/854svobS0TJBjtloRFRONX//mRXR1dYn4oEeDnIG/0aimx2iY7SvPPblTZlYhVq/ejLr6VvEdRkTGicOgo7NPotKkYL4HZS0HNb0g4ox+HG1QyQOyP0UxAwP9mDplBo57qcAhf2dqma/fWXExuTU3AkvkiQsJiSlYv2ELqqqUGstEmY2btqKzSykhI5F1nww1Ei7dUUbVIbgcRJZKHB0LWbwvbToirL1jALV1bSivakRufili7iQL4PKLK3ElLAq+/uexcvUGnDzlh94BM8w2B4pLK7Bk6XIsW75C3pFIyC3Iw3/+5tfo6OgQn6TVYVFJoIa/UGSO4UvVmi5jZxmZBdi5Yz8SEjPAMA25UkVFHagDBF8ORWlZlbB02qa8h9s/6Ims+wBzn7Kh5JWiLDoklZeAhh5trMCz52VkmY3jHAWXQ66L+t7WrhQH8nS+IEfp7YhoHDh4DFlZueJl2LZ9lxtZmgpICcSFmzoMmSkkyRvxBHIKuiHVSBgl8cRQOIQFudDXPyQj2EbXD2NHShS4lQJ+7TcNe0D4GMofxZBI9Q7UNzaIK4n9qK6rxosvvYjOTvWOTqcZLtAw5j2UqHB7UYw+Dw3akJlRgFs3YxEVGY+21l5YLTZJL6B2ffdeCqprGgRJtE/ZJ42sx1IwdEieACQgu7uJrAW4dDFEvOd8gSGz4tF058TE3hEvclRUlCCTv9OtwpaTm4+o6FjcuBGOnTv3oLtHWfjKFUWWoaPBD+4ZRHQ5XO48QT3I6HmQzR0GH75Wn0OESQiFic68h9a4OIINOSpIou+TkWqxb9Sex9noECYFt7a1YvKUSejq6pTjTJ12uujSUr/zmTyP18lG88BiQ1xcIuJiE1FaUiGJONSMyyvqUFRYisLCclRV18t1vKkkmI6ws8b1uqsRrrrLTjAK2tLSjklvTUVQ0CUJeYSH38DQ0IA7FsOHdXd34+LFi7h06RJaW5X6ToToxmSaFctXuyPL97Ox4fjQf9dxgu3d3ovvrUwF5VVgktDLL7+Mzk6FLK2tjby/Yu3qjcmKr12/hbS0HPGd5hWVobSiVgZxxO045OYUo7KiVmJhvMJt2HMAGmyQ9x9XdSeQeTERR7dTU2ObyCx63Jl65uXlhevXr7tTpEm+bBSQN27cgK+vvwTyFFkzO9aJuroGnDh+SqiU54580ffTdyJLvxP7WlpaioULF0rmlvTdA5ie/dbIIkujokVHsJ9/kCCITu7LV8LF2GdMKy0tFw0NLWIKKDGg2KnAzOP+4yKLqi9ZIRFFhJWVVWHim1MQn5DMvgoimDDD5E7aYGxKk1G5D/fuJeDEiZNobGwShPJ3hveZ1NlteDk8X/L99plUpT01/JyQkIAVK1aIscx38Rz5nn3XyOI5tNPi7iRh3fotqKiuF3fb3YQ0cQx3dw0iJjpeMqkYj5N7Gm4zPs/z/uMii5gmwrTMysrKw+uvvYn4e0kiw3hzqvOkojt37kiOu+ogZ5goaV5YWAwfH1/U1Sn3EtPTNm/aJohWnfvvZ32egHsvnwkwbmx0XDOlYdOmTWhoaFCeH9FWaZzf/w6eyOLgZY4h7dGLIaEy+BnDSkjKlBSIm+FRqKwcTpHQMJH941CWJkvpLYD09GxMmTwDGRlMq1L2ACmKJMusp3PngiSgx/PJPskC2AoLS3DkyAlUVdWht3cQJ477uHM1Rr7o++m7ZoMyyp1OSWwpKSmRASqzYzyA6dlvjSyq73SE37wVg4SkDITejEZ1XZMYxyFXw9HXO4DUlCw01DcL8nkPxc3UtKrHpKxhBYNAT0hIEQWDSPNsSgGxIC7uDnx8GHDslZ+ZasxG2ZeSkg6fk77w9j4jvkW+rPrt/lHp+dL/rz9rZGl1XDps/CPFMKtWADoGZRFpFqsNoWERogU2NrfhatgtkVfZuSWormpCQX4Z2tu7hTppp3KQq20EG9Rk/uCeigXZn7Kx2Gl+jo29h3nzFiIvrxCxMXFu4cvrKdvYkpKSZNJBd7dCGP2CZKNsuTl5mDZ1Nvz9zsFmnP/gs4cnu70fflOjXbE6chDdJ8KEyJLNYJf6N6Y26Hz4wSGLUFZensq9iL2bhLaOHvB4RkYe8vNK0dVlzMoRz4XiWCPv/0gyS7Mydjo09CZmzpiDgoISXL58DQkJSW6FgmlYRChZZ3x8MphKzIxVNqr92rCOi03ASW9ft0Ly/5p63tPzx2GDfHf6Sy+HhCE9Iw9mmwttnf1ITMkSuFVV1ovq3tMzIHBTYsdIT6DJ4XH/h+QNKiOY1MUbsJE0r14Nw7SpM9HW1oXOzl6ZFcKZIcyzY+O5+vzUlAxJkWbWLi1EIpKIv3snGdFR98SKV9coVZUj6Ynb9FS8EX0nIzGYiXAf2lmnzwSib9AiEfQbt2JgMttkMkVYaITAk9yH8OYmarsY1yq9jnAZl7K0I1cji9RE32CX4dejJkhb6nzQRXQaYXvBmoG4tLRMbNywDeVlFXLYbHKIJc8Omk06B/79K7PGpTqPke95rlYwOM7pqWdykK9fEFIzc4WisnNL0drej57uQfic9ENjY6sGm4gM3utd2FkqwZNYJ5s7H3QJE9+YjLo6Facij6ZQDAu7iZ079qK1tV0eSjnFjSPi7p1EHNh/VBy5pM6Qy2GSmWoxG6HrEcLZ86Xf958fAVnUls/4BqKgsBzBV2+gf2AI9LbHJ2ZI3uKVkFDhUgSc5kyEm7y7x/0naIH44F6TI0e9/mwXB+70abPQ0aGmnHJ6DxszTy9evIx9+w7JRDkeU35F+RnFhaXYvm0PKsqrQRcL04glqCf3fn8pFA/C4iH9exQFY9CEs4GX0NjUgaKyauQXlWPIZMKNm9Ho6OhFRnoeurr6DfZHiqLJwyzf+xWYcWUWEaUNYt7A5+QZzJgx223Vq9kZpCLFoSnTOEGNPkThv1QQyQtcENX9uNcprFyxDrU1LbBZndKhJ05OecqncWQWXaJMcg06H4Ka2iYMmW0IuRaO/kELGpo6UVhQIdogVXelNSutm7BWadoeMsuD7jxp0H2YQCbrYqNycPq0P6ZMmYEDB4/g6rUwMe4U7ShvMT/HJyRi9549qK1TOeJaQ+Rv+fkFWPD2QpSVlevLnjylwgNZqjqGCpTeP+gMcIIxNTMCzjJnvkFESVpmHsqqGXZxIisjH9lZhWD03HCUCFworxhX1yES3nuCIc3uDyKJDFGHSB1CXcYsCyZ0zpg5B/EJKQgNu4WAwLPoH1DZqww9MFrK3AlGVPfu34es7CwpR8DxwT+Hw47TvmdQUFQgPNnNm59QueWuPDOi/xIQM4JiFAdXroZL1heVjc6eAVy6Fi5ILC+rQfiNKHR0cL6WUru1fiDRAk+ZNS6yJMFTEQE9Dpu3bMf8BYslG5cPCLpwEf5nA9FleCwY6eQjKRyvh4XB64Q3Kqqq3FQ0ODSEE94+aGhqlkR8yof3vRIxAhGe/R0PWQQ8g6/eJ32xddtudPf1w+pw4HZMPOqaO9HZ2Q/vE2dQX9/spiylvitM32dnjYcsQp5yiY2I2LP3IObOWyh55/rY5StXERh0XhBARDF4xxHElpdfgCvXQpGZnSNINFksOBt4Dtm5eRIE/EOgLE42PHzkONLScxAXnyzBxbqWLkTExkvkgS647i5lpxJmFDuEiwzkx6EsAl/CI+S9ZjNWrV6HKVNnoKNzuAAJH3Ax+LJQTG09ebEDA4ND7gkBNbW1OHTkKNIzqQGacczrOCqqVILIU40swyru6uqV1PLevj6ER8RIVlffoBlht2PB3zip0DSkwkuENSmL7QE7S44+wj9ezkym6TNmCxtkjIf3pP+LGg9D0bcjIuHtcwpEGM/n7A3Jr7M7UFJahv0HDyE9Mwtex70ljZoy7klvShKP8h705BipEEwzZ+pdT28/Glo6ERoeBdPQEApKqsWRy3gWJ0soWaXsWg5ipiK4VWkAE8YDlpCkcRKzkmbNnoctW3fJrAodqddAJ0XFJyTh4OEjwhJ5mUzttHNOkxOlZeU4dPgoVnLUPrwAACAASURBVKxcjY4OncMwXg/e378/DFkcsRyPnLC3ZetOSd6x2l24dCUMXX1DktSZk12EtNQc0QaJLN1IVapxIKjBMK42KBg2Tmfwbdny1di2fbdk23KyARHIxtsxkZONSfacUdLU3C7H+ZuFqasMi5eVY9r0WTJ5gd89hfWT+Hk8BYPvyGImR456IyMzT5BX19iOlKx80QVKiipxLvASWB5JeS9UlIOwEPg8jsxSmomahMYct9VrNmDrtl0SRDx/IUTUUU5qY9N5cpyxkZGZg737Drnn4+pB09rWKaOM4RMi8UlEkGefHwVZlEd79x0WLwZ9rZzyc+1GJDp7TaipbsIJr1Og1534IcKU54feixHxLAOd9xnEPMaLeLGnI5f1lmbOniczQUimrOVwMfiqzA/Wk6Qpw8wWVXeClWSOHD3hno5KttnfPyjTV6n287vizU+gt90wjMcyisXlbozQIZkYf1jmKOcWlIiSlZCajYbWHnR39eOUj79EzwlzpQkquCjD+DE8GLwBGw1jzgqZNmM2Tvr4unPaCXBO+Pb1C0RVtcq45SWccslWVlYp+e5EHBuzd/fuOyjTavj9DwFZ1ALXrN2I1vZ2BF26KuKiu28Id5PSwd9CQkLdsT1tJrlh4+HOmvAwyiKiFIWRJF1oaWsX78Wp034S5Rw0WSVkzRsnJqUJS9Qp0lRBKUzZGhqbcfDQMcTHJ0qnmI3LzF5JuJRU46ebslhwbMnSlZKbkpSajcpazn40I+T6TWF/9+4mu32tns5vpS94UhZ53SibPkQ2yM9snd3deO31N3HihI8R2lZTUfkbkZOalo0dO/fJxDBm4ZLquNEjz+KQRBins+7bf0QoTDmJn+BYFpNbdKHjEV4Oups4CYawY1VTuukYGukfsiD0ZhTaugdQWlmPkuIqpKcxpVxpf/S/Uk9QLHGkzNJYGbEf/mp43QEh2enTZ+NS8FVkZOa6nbhULLiRjnJyi3D4yAkUlygXE50fRCQbK4S9s/egVBRzT2AY8ZKewvtJ+PwwZAnCqLr39YudRXuLAzTsVjS6+ixgsieDsCxiqSeGkw0SYaQq+lHvczeNDZBhgiN1sTGTdtbMubgcfA3Xrt3AmdP+7ogxkWsyYls1NQ0ySTwzkyNGuU6odLDV1jZix/Z30NPTb7DYJ5uyRsLPzaUIMgU29Pf2Y+vW7TLrk0hobulAYmoGhsxW5OaV4OjRk+7J9CytILn4RgKORhbvO248izcfGFCukNKSMrz80itIS1PJHlFRMbhwIRi1NToUQipyyShhqVUvr5NISkwTNiiYkmpgvThy2Av0l2l5KLzZI+zwJH+Xl5IXo1am3ppK1aZNm3Hy5CnJIWQ9qFN+AVLkpa6+Bce8Tol7jmdbmHRkRIn5XYdIeN+HIosnk3/SvmKjPcVJCSzpoxtrMLHUQmGRqupJCmNf2RobW6Sc6s2bkfp0CQUc2H/Ynef+JCNmtL57IkvPfOnr78PKlauRk5OLhMRUmetWXlWLtKxc9PYP4uq1m25tkE5wgo9OXLb7kDWSjIe/K3Vdp4/xwqSkFEyeNA0pKRmCRC0UU5IzpMhwUVGJeoBho/FLeXm11LaNjbkjv7W2dmLH9t1u1X34eU8HO/Rkg5yiRIR1dXZh2bLlaG9vlwmHJrMdnOUfeP6S5MxHRd8VEUIkkRiplGlk3ccGxwYWL1BGsdb9s7Jy8OYbk5CamimAV8JQjYDsrHwpNMwq02xaQeHnpqYWqRx9/doNQR4rS1PoqvOeDiRpOLpf3ENmUXXftm27zDypq29GVnaelKMtq6hGW1s3omPuSfhJKEo7xw2T5pGRRYCzKVXShbt372Him5PF1USvO+WTDvkTscVFJYIwnVpNytP3aGvrlARRzvSngkI5qBD6lCPLCXS2dWLDhk1irlDTYz0rihZO3CsqrkRsXKK7koE7hW1EdhOB9VCZpRQAxQ7Jn4ksJniyvLev71lRxRU6h/83NjaLlpienuU+qBHGXASWv+P1RDbvPxrff5KPecosrWC0Nbdh1ao1yM8vFNW9sKhUZutz0jjLkV+9Gq6q3TCqTAXDgJzAQZcVH0/BUMhS2gIvpPZHNlhSUoHc3EKpx15To9KjyRJZvpuNmiBLL3ASg+fEBP5WWkov8wUpisjvTzJiRuv7aMjq6+nD8mUr4O9/VpQH2lfnLgTLDH/WjGe9EGqMbEPGBHB+pp31GAqGAqbyNLgQHn4Lr736hqjdvBnz3Q8fOo7MDKryzK1TyTXct7d34eDBYwgOviqhax7jhPDi4jLcvh0tDl3eQ/P6p2X/gMxycV7XEHbs2AVW4+Y8rIFBM+LuJqKnr19K8l2iv9DQuMkGqWDIDBWPyXTCBscGklISlLtJ5QOwyvSc2Qs8gG9HRma2FCtOTVXVVFQWLtEASfZkjfPDh4+7BxwpMi4uXni0otynXGaxGkB/P3bv3iPZyvSrco5xb18/Yu7EizHMQv6cw0UkkY8xcqHExPDEhEeUWYoNUpUMDg7BrFlzpXSoTpsiUiorq7B3z0HExd51Kxz0XLAxY5fejksXL4uxTO9GZGSsdI6/j8ZKnuRj7lEpOrgYSjLxbu/e/VJT+F58EnJyCiSf5fLVULS0diIvv1QGLx3fWsHQkeL72ODYgBFYCzBJxtRiAgIC8V8vv+qeKEfWRictW21tHc6c4WIySnX3lHccSczUPXM6QGaVUJYp7/KT620fC24PIIscpqsH27btECpirsX5C8GSz1JZU4e0jDypg8F0NSKKpKHIQ4mIR0aWZlNUz4kszhaZNm2m+PdYzJjqOjU91XHICj4sOp+eli3lUJXqrtR7GtdXQq5jyuTpSEpKE/lmNg3Xjhjr5Z+046Mhq7ujC4sWLpYSQoQZvRj0YDBdjwVLOIWVMyvZhA1KKhphO7wMIu/70Ck/pBxdBog8dM+efVIU8vbtKOzffxipqRnyAFIXz2WjZ5maYFQUZ++raais7kmkDg4MYvu2XcjKzjdsNzV6xpabT548k5LhNGgZIlGF29Db04c5c+bh9m3ldmP10tDw21IzvrikEtdDb0t8kPBj7SZWoeYgpejR02BFZsmBEVMs1TGerKiCNyGyKCRZG5eJMwUFxVLYODVVUQnPZTCROGtpbcehw8cRFnZbKnzyeqKSXvlr18ORX1AiE8p4fOznP2Tmxqj9fb+dr+DHQcoFClj1k6o7BzCVttiYu6IRcyD7B5xHb59KPBoyW8TWIrKYY6mnwbocjodTFh+kWKBa1OTw4aPCxjiBjo3LHG3fscdNYUSYxVAs1NTM6wg8d9Fd9of1CC9eCgHrDbLmE/k3kfU0UdbwuygRQRgyjsdJ8Xl5BUhIYFTYKkVKGL1gdljYjQj09ik7iyVXaRhryrrP3TS2TKAsUsiiwUss79r5jpTx0YWMaX9VVVXj1OkA3LwVLbMiiMQ+Y5T09Q/g1u1oSR2mdsONtd7pG+NzlUwbbQbG06B4KPgRHvTq7Nt3QGQWp0PR1UbxcuUK1xjrkyKS/K5Vdx0iIeIfS8EQEjISXdav3yj1cckSOWK4sdE5yXqDoWG3pYw2kavLhbNMKWeceJ88JSEWhvZZVIpskZePPViedIRpyDHyUAmq7nReFxWVSYiJ7JALAzCelZKaJao7RYjAxIALuc59yBom25HCXJOxklt0h9AZyfq4JGM2Uh6TN/kAGnkcKawqreuZ64QZrqiQkpopkxoWLlomkVKOIuZpkM2O3Ycn+TcFP4oGVtZ55529YnOKCeQfJDnu4tEpqUJMbIJog4SjVt8JX3Ki+9jg2IDSyFIjhO6QrVu2y8KZ9+4lgyF7QZhY3Ooc2gpxdxIkKYY5hmy0xnWBYvLoRYuXo7SsUn7TpsHYfXg6kMV51suWrXA7vvPzi2S1CYqBisp6qZg2ZGjORBZh5pblRkauaINjA0r5+QhQbkTWmjXrRBsMDDwviZ5RkXEyWsjSSEUcGVw9QDwWwdfQ2sbSpMrXRezQuF63frM7b4Pp1u5OPeGJMw/CUSUakXOw5OzGjZvdqntv76Cs40IljBPBL10ORU+v0gYJQ+ZhEC7UoTVlSb3BsWWGkid0F1GRYAWzxYuXYv26zcK2mB+4c+deWSBGSoWKjcD8QpXzHhd3D2fPnndXnyayuPwQM3QZjGTGEzVCCtOx+/Ak/ybMQ5wJTDS6fPkKIiNjxMFNimK0va2tXYKOkZF33HYWBz6pi40D4LFklrasuSD05MlTsW/vIfEI82acCXI28KJog6y8zEaWp3PeIyJjpIZ7TY2qhsY5W8x/LywqF5tMa4MPjsonmf3pviuORM7CdIeLF4NFwbp+/YbAj5zq7t0E8Rsy35LriBFuWiPUA1hT1jhsUMkshWGXrO04f/7bsrgzH6QznpilRKPu9JkAdzoV8dY/YJJRlZdfJNMzOaOEbn9SFgsMs3FFoKcTUXwvBT+q5MXFpWJnsQpPdHQc6Mym8pCcnIbm5g6ZEcmMJyprWsEgXAT2jyazaGPRUctJXi5x8y9ZskxW56ZqziZs1fCsX78ejkOHvYS0+RvZnCbn3LwiKReemZWHjawz2K+Mao6ipxlZpCrCihHi06d9xQtEI5gOb07QYPXOgsIKD0euymwimjgRkZPpHoOyFLKobtJGIGWxXCqjw3RCEvlaPe8fNCM65g527tqL+nrF9qiyk7S5VVTUSLlwzkdmh0WQGgupPZ0IG2aDaWkZ2L59pwqDWO0ICbkuJesYWU9ITMdFTlM1SrFzTgG1wVEpS/PGkXshQScTPJWW0tLShoULF0uIg8urM+mFI4eNiR8EPqmJQpQURtJnI6LoM2QjZW3YwIVZVGYTj4587tPzXV5ZBjSzwtasXouS4jIJKbW3dYmCQVOH6eaU+1qsEJZEFtsDRvHYwFEjgxeRDVL9nDp1htQJpJw6HxQsORhdugozqcyY3ZiSmo4DB71QXqby3UmBfDxJf82a9e5iwFyaaeznP8maIPuukeUE0/N8/QIQGhYOlghnKjkDsFTdu7r7cTuCwVhVVomDnmOblCVmjUt5MXjDh4ZIlJBUQKP6uWjRElwIuiT6P2UZKSwwMNBdvo42hZZjxUVlCDoXIsafYMooZLxt20709/dJR54GG8utSShgKa1CbEaFLCoSnOoUeiMc1bX1MrGQ0QcuwcRFargaOheYEd3AcMFpZAmhPJ6CoepZcAXvSZOm4GZ4hJufkufGxsbC29tbAo+KCpViws/5eSVSnu3OnQTpOQv4Hz/uLbXeOXJIVU+6vBoPWZT3zAq7HsZqaAPijuvo5EI6ZkRGxcrk8KRklYNBYiRlyaadBI+KLA4WrflxFdA33piI0NBw0RIZqmfjyImMjBQksM67bmaTXUoL5GQXYP36rTKZobOzC2vXrpdS4VarRfHkJxxhD0MWWeHQoFmWsr9zL14WTssvKJYV7ljWjtOm6MiNir43KhuUgeyJrLFlxrDM4kObm1swd+58qZFLGcamWR7vkZ6eKfXbmYvBxhIOXIyHraqyDnv3HMKpU77w8vKW1GFew7CLprCx+/H+ll0inAigERu/sjnsDqSmZeDcufMyOElpXLOFNUVoi2bnFCEkJEzcdjyfl5ENuuHxOEme+qHku9OmzcCFC5dVdg7jLxKcVMFDRj9LSsqkalp1tZoCRIQ5jKmqra0dsv6It7fP8CgyWKG7Y0+g62kkkvR3DTcOxsjIaGzfsVOWoKLhW15RK85sen04P+vK1RtuZGkFgzBRyFMuJ9533PRpXkPhR1th+vSZuBx8FbGx8eK1YL4FGzUZjhieW1paAX//QFBdZbNaWOxQPZgr/LCeLsMtTzKCPPuukTNyr5FFr82tWxG4ej0UAYHnJLWB8oqhJGqDLBgZG2eESJjcyZCRQG4U1X1sAa8UG2p4XOEgOztX2CAnHdC5yyk8ZwPOu9N+2Tn6+tiYn3Hi+BkpBsnv9IQwdlNdUw8ud0F/I1+CLz32858MVxRzI0bb+M5qoFtw48ZNWeHo0uUQmVvNYpGxcfGg7cqV7BIS09QsEiM8Yjc4zruIZ7FKp0MeOGfOfLBAsW7MYDp//jxaWlrkkCZdfqmsqMM7uw8i4naMzFHiMSLxxo1bYq0TSX8Iqjvl8oULl5CVk4ue3l7JGSSy+vpNiIq+IwlF1AZNuvSfkeFERHvOKabMGZcNEsgEbFhYuKRTcXkKKhbMyKWikZmZiXPnzkllTj2aeA0fVlpShbP+FxEj2o5VkEXvM19AU5UnS3kSPz9MGyQciJgrV66hpKxcUszu3E1AbW2DqO7XQ2+irb0X+QWlYiyLfWUoGIQ5Keu+EMnYAFJsUByyDpewL0Y7q421hbUvix1iOtr+/QdQVKRcTERUrxFMa2vtxrmzlxAREYuwUK4GdFfYKBGmkPr+1vbGho/q90hZpb8TBmyU95wjkJyaJm4kllegNki5zSXaqWCkpbN8ONeOVNogLyWy5NmPow3ygcQwKYKRYk471euMsEO8IRuznI4e9RJFhAiW64zV+cxmh8zJWrZ0FeLjk2S08TLxfT2BGqAnAjVyRu41sogEIuvgoSNgFVMuaRETe0/yB+m9uB0RJ5lhOn1aaYPK+04YPjJl6QcSWUxQ1KnTgYEX0d7RKWyQHdflwktKSrF37yFxUvJBLOZJ1Z0Zu5wMzoWoaQIQSWwcXU86wsZjg0wbv3UrUopjxt65K2tntbX3oKS0Supg5OQWy9paRBYbIaNXVH2ADZLcRt8UGyTCODoCA89hyZKlUss1NuaeUAqLRLHJTQ2y51IW/v7ncOtmJJyka8a7jFyL6Og7yMzMllABj1MrfNKVjNE0QR6j/GZjKsOJ495SFPPESR+Z7mOy2EB5xSBsZ9cAklIyYbMpjxBVd268mnC9P57F8IZMgjOQ5uIJau1dPc2fs8v9/S9i7dqt4CJd7EhCUhL8As/KUrDsFEcEC/Wy1dY34ejx07gQfMWdAtDTNwBOcWFtXKnw6XKAi0iPPlCe/OMMDbHRrXTGzx+FxSVIy8hEXiFTx21Iz8xBZk4+BgcsyOSCMmaaMgwpuaRsrY5IaGSpBTo5E0Rmg2hkMYmF00/UIs+8AdOc39l9FAsXrkGfEd9iRzJzs+Dl442s3Bw5f5C52bSdALR29MpSDgePeEmeAe21W5ExSEpLxwDPY9lwruo2JmU/2b8ZhCUZXaxeWlNXL6skBJy7IPKqq3cA18Nvo76+VSp5mkwKWYQriYFwYdPI4vcJgqgxkEXjjCo6Nb89e7wwfdoCdPcOyHryBtdDXlEBTvn7Ijouzu3Xon7BR3EJh5On/XDyTICE+znTLyElDRa7HVYuC0Hx+ZQjiz5AKhf1jU2SyZWdW4CsnDyZQZKSkYWsrELE3+N8NYUsoa77OJ1RbGs8ZJG62PoHzDhxIgDLlq5312eyG5TH32vqanHg8BFExcTK+bxK8gjFq2HFGf8g+Aacw76DR1BQXCJs0MK0gD8AZNEVx7r3585fkOLOXKXO92yQlGLtGxxCbEyCLC5NZA2HxNQgFnlueN0fgbKYs85Z+Fbs3HkQ06cvQGFJOWrq1Qo/FocNZpuKcNI6P3DoMCKjYgRh/McZJdIBF8Ran79gEcorqzBoMsso47r0zqc0fVqzQWYtnfH1w959B8AQEUP2iSnpSErNEOpircFbN9VkOsKKlMVNt8dgg5zq45A8jLlzl2LVqi3Izi/BsZNnkJKWJvdjBq4A3eWSHHefU364HHJV5b8JZTklp723d0Bq7hUWlUjtV/aHBfmfdG1wLDaukUUFwy/gLDKysnE7IkoGaf/gEPwCz4NKV3VVo8gsaty6aZnlqQ2OS1maDXLGw9q127By5SZxOBYVl2Ll2jXIzFGLdHLtEZmtZ8x8ZOVpVkTr61deCi6QwtRpVmBm6VYiiizwqdYGDergXDYqGG0dnbgVEYnCklKhqNvRsaiorkNLc5csHKMc24qqNLJkIHiyQYol2QwPuMPJPEFDnhjBMBqvCxeuwrJl690GcHllJc4E+CH2Tpzkt1NOMUebjS6V4JBQWTavoVFFj/sHBvHOngNobG5VqVZ/KMgaHBQW2NzaJsU1r924hd4BEzq6+xARfQdNjR2yfpZ2zxF+1JyJKDoc7mODdvEyDLuNaDG5xM5yiCVN/skQyZYte7Bvn5fUyNMstbOrC/5nAxAdGyNyiA+SBczE4KWb5Ra8vf1AhDFJhLVxu7p7RdCSfZIix2IjT/pxzQY50Ll4TnVtnSxEcDchBc1tXWB9Ycqu3NwSoSyq7mxayRBEUVP2pCxP1Z0nkLLMlkF093ajpa0NLNzf3TOAjRt3Ydu2/egzCkVa7aQ+zuprhJ+fn/gOyepIwky3Iq+TkHZKJoKCglFUWII9ew54+BWVI/RJR8pY/dfIoj9w1+49iLt7T5DR3tmDmLsJohFX1TbIUu15OcVCTfQpaL+q4MKjwgyfM4FAJcIozCjs7Q6LIKurpwstrSpO1dnVi0mT5mDr1r0Sf+H6IgOmQTFq2QMmbfr6+uH8+YuSGygTDoyyC4wS37uXAt8zZ7Fo4TL3shYUvGO96NNwfBhZJqxbvxGHjxwTEcJlPuLuJaK1vQO9A4MKWbklgizP6jzKhTeCDao8iWFkKccRp/STDapQfWVlI+bMWYqDB08i7GY0ouLUKKGSQHZG4LKFht4QpPT3DcJqAchinYaSw5pNLCXE2ntstD84etzk/pQZx8PIGsKOnbtxMTgEtyOjhCC6e/pw/tIVDA4NoiC/VFYAZ4DX8NaJ6k5kic/dkw2Ssogw92h2aXeT0tYon1gr8PdvTIeXlx8KCotx8OhxXLwcDBuxYThkuSfObt2KklxBCk7drBaHTMbbumWn2Br00lMWUgN62lV35qns3LUbNXV1OHz0GPr6B4WL+Z87j9b2TlneoqiwQqLxhAnFCJt7EHsiSwwxd5UYJbMot5RvUE2OY27b1Gnz4ed3UW5U19ACv3NncSGYSR+qJAAfQn7LByYnp4MLcVZVqQkKDJNQnvn4+KKnu0869jR43N0DfBSuoCmLqjszm7g6X1FJCRKS0zFgsqCkvBJFpZWoqmpAcVElHMaqPgypEIZsEuOiEkaEibtplAd5doJqJCcwL1q0GGfPBsqo4I24zuPly5cRfOkC+rn6N91P7tx1ICszGwcPHJbJCDyftpr3KV9QhTdZncr1YlNJ+FZOLbK7wHldfEn67pkQZXU4ZU9fo5WpBJStTDw1zuF5rKtudynNUuw2I1zHz2TjMj9XpsqS/5NbcACq4ipk3nQnO1w2WB1W2RyMBsgx9pG/GedzZofYh8rvyX5y5pPYi3CCnk67RBKMZ5DFS+3FXixfvUZ8o+Qkx06eFmc4zZwroTdRWlom8KUMZ9PchpSlPxOu3B6S6670fN6gqqoKc+bMwc2bN4U8eSEb5U5sdBTO+HhDJii4nO6cQD4sOzsHK1etlyIlfPCKVevdVZblBk/hP408QTJc6OzpxeFj3igsLhclgu66iOi7YhhnZufJgK+oqHAPdIKEsNMI8iScR0JWWVkZZs+ejYSEBLcy4ca63SHUdeTIESnKwYeRxenIJ3M2uLRD+M3b2LRlJ0rLKtDc0g4uzdTY1ILaunrZGELgwjP0HXKNrZJSbmWy3GBpeYXEg7h+JONhWdk5SMvKQXJ6JlJS0pCali4ZwRkZWZJWwJwQHmOuI+sgctGa+IRk3L2XhITEFCSnpMqxpORUofz8gkIpdV5UVIzCwiIUFBTKBDge5xK9ZWUVsgBORUU1qqvrJOGlvr4JDQ3NaO3oRGd3D3r7ByQP0MLlQDwGIZOX5y5YhuCQG3KUcDvm7Q9W22HAce/evSgsLJTfiCAih81zrxH2UGTxJN68pqYGCxYswIULF5CamirxKfqyrDaunKoY7PXr1+X3zs5OlfTJijJGmnV1TR2mzZyL3736BhYsWollqzbg7cUrMW3WAixYuAQLFi3F/IWLMf/txZg7fyFmzV2AaTNnY8q0mVi4ZBnmzF+IydNm4vU3J+HV30+U7fU338Lrb7yFV159ExMnTceMmfMwa/YCTJk6C29OnIo335yGiROn4803p+OVV9/CSy+9Ltsrr07CG29Mx2uvTcUrr07G67+fgjcnTsNbk2ZiytTZmDJ1jmxvTZqFiRNnYsbMtzFt2nxMmTIPU6fOw8yZi0QznjdnGebOXY4585Zh8dJ1WLthJ7Zs24cduw7hnb3HcOToGZw6HYTAcyFYuWqzHCuvqJGE19KyBqSlF4gcj4qKFPhqBHGgeyKKVKa3hyKLJ1GFLCoqwrx583D69GkkJycLK6OqKZm4dhWO5sMyMjLQ3a0W7qRhTFzxHpyXxbpFoWE3cTXsNq6FReBWZCwio6LFSx8RGY2IqGjcuRsv909JSZHlCGNi45CSmiobn5uUlITk5BSkpKRKRlVaWjoyMrNk/hOngpIScvMK5DvrHnLLyc4DM4EzMrKRmZkjVV1YnJHVXXicVMeScvHxKbJPSU5DakqGKEmJiWlIlN+SERmZgOvXo3Hx4k0EBFzB6VMX4e0dhAMHTuHw4TM4esQP+/Z5Y9u2Q1izZieWL9+CRYvW4fXXpmPFik1SWSYw8Ar6+lizyinKGjXF6upqETOEJZu2dwk3HtNUxf1DkcUTeAFnkOTk5EgReVIab8gRwL0eBbw5mx4Z5NkUoixeotcokROegn98U3IrKhgU30oTVolBXACGSwIyysDV95gjyJW/WfOjtrZZ6lsxTaKopBytbe1gklFtbY1MnicMCU+yQ37W8OUxbuMiSysTnjDmTfTGmxCBNKK1UBw0DYnmRe2LGhW5MKdfmq1MWuTkZmZE8RrFROXlqdlRA6IGyA6TKgkU3oN5CUYiidbuRICLo1PZg+p3h1yrzlFamc3Q4ug5EG1OtDhlkjBPgp4x9oO/qecpJMjaXtQ6jWm2+rsnWwQaAAAADZ9JREFUHJR08Twy9me+E2ODhBNz3NkIN86/1rNpCFONJBIJP2uYcj8usnjBWBsRRWRYrBZRYblUuxQhMV5c4lyCBEMll+mXalRyZMrmoQ4LMEd8F1WeQBttM1RvO+1C0JinAm2D3UU7kXkkNticaiCZrWZmfIj9aHUoW0YcyazOJn5ONXDYZ35nOhibDC4jZscBotRzOlhdMFktqu7HaH2TSDoHgVbrVf+GzIOwOsz0/cDmMAsyNOV4IkZ/1r9x/5D06bGRpJHHG8iLCkXY3aOTSONI5m98QY0Evji5peemf3t3e96b1Eok0U4yweGi0qPScRTiCHibKEJE3JB1CGJLCTBJiUoDY9/YXzMRYNRT53UCbKe6nui02M2wOjg4iUwq6mP9KY+52cI+GX2UvtlgdxLJZgya+gyZ9GAuCmFM+GpYc/+ekCU3NNjXgHlIRiFfmkvkcYSy8XXklR5CoZ4derzPTlgdfC4RZIXNaRLEyah1WmBzWoTSTFZVcYD9ISIsdgKLI9sq300Wk3xXjFK6Lf+sdpMMBlIuM744COwuIsoKu4vXMD1BuedG2zucFpgEIWZYbP0YMvXA5eLSi/1wuGgEW6XWBetdPMp7vzc2SBZCRy4NZIcNfYP9sgoA35QeBE1hzlHyA3XgZrxOerKB0T5b7VyJnJonx7oa6RwowpKlZ5Q7dplyw3pSupktDhH2Qi1WC7p6e9Dd04shi1n8eFxifrhRZpJyLbIJ0pxkt2Sx5CKeG4+pzSlebCeGzAOwWE1wOGyw2RjVGJI1BvmdRYtHe6/Rjr0nZBHQdrJAeoKFv5OugAHTkMgyYZFjJMSoZMXxSyuM1un7jonMITtTck1WHDfmRvE8liifPWe+2Hjf+NZ38NakqUhMShE/JpUL5kHyPZiZ9cwPfojnXvgFlixdjud//gJ++rPncC00VFg6WSfdWmSlwhql5AFdWCMpa3idRioTeu40ZRATZgROLrUmmY4Ia/k02t7zXd8zsuTpBrtjVLSkrATHfbzR2d2lWKD2PRreY40kvX+vlEVbzoh1iuY2OMgBoHpVWFiFGTMWSWZWfHwmjh71xZe//G38+Me/FoOU53F6Lfft7R34wQ9/gk99+m9FnS4uKcHzL/wKz/7HTyQRiLc0bqtfedw9+0Zgs7Fu09IlK1FjrOJH5zbnAngiY7zPExS/HJtn8kG8CbFOwHJOlu4Af+vp7UdxSRm8vE/gtTfexOe/8Hf49F9/Vhy90sv/C/9o75CdUUOjwclG9fjmrTgEBgaLE5nHrFYX1qzdho9//PPi4uIxFiXlnIDunn689PIbePW1yfKu/G3/QS989ev/jPaODqUV2p1iN3J+NCtKM6+faQpMe+jr54TuIWGtOnWa9/Bss2YuwPPPvYjkZJVoxN/GG6yev09wgYKTm1YFjL2hjWjSVEmIw2Orvr5BlqyYPPVtfPkfvoMJE/4Ef/rBj+ODH/4kPvPZL0oudz19Z21daGvvFl8gS4jTL8i65nUNTeDvdXWNqKmuRVlpBXJz8sWfR39felqmzEtOSkyWuWFxsXcQExOH2Ng7SIhPFJ8gfYEmc7/IDJ2roHRPFwZMA2htb3ErOgQM5ei5S+fx8U9+ArkF+fLGVIO43YpKwle++j2E3VYr6PFNN23bhx8++4LUWuT1XCh7+65DeP4X/4Xf/vZ1/PKX/4WfPf9bTJ42H6+8PhVvvDUba9fvxNoNu7Bl234EBIbgfFCQbGHhEfjNS2/in7/z7/ju93+M8NtcilHRq5g7j6CATaBtorZhXqvjJ0QUDTY9w4FlgK5cuYp1azfgJz/+KSZMmIA/+9AnBEEf/Mhf4cN//il89C8/i4/8r0/hH776XXz/336Kf3/2Z3j2x8/hhz/6KZ75wU/w/Weexbe/+wy+8a3v4Zv//D1865vfwde/9m185ctfw2c+9Xl85MMfle2vP/O3+Icvfw0f++gn8cE/+3P88R/9Cf74j/4UH/7QR/H5z/1/+MevfB3f/c4zaGyql1QEpa5ztqCyq9SQo4FNI1SFH5ineNrfH1/56ldBHybPYWXzQbMDh7z88Xdf+iYGjJXLk9Ly8MsXX8OS5RswYKJdBAya7DgbFILFy9ZhzdotWLZ8Hf7rlUmYOHkufv6r3+Enz72IX/7nq3jmh8/h6998Bv/41e8KjCZM+CP82Yc/gR/+6Of40le+hY9/4nP4zGf/XjzxQl1aVIyzn6BH5AN7jwuV24M57ybcvh2BWTPn4Nkf/Qc+/7m/xYQJH8CECR/Chz7yV/jQRz6JD//FJ/GJT/0NvvntZ/Cjn/wCP/j3H+PffvAsnnvhV3j5lTfwxsQpmD33bSxfuRaLlizHzFlzsWTJCinj+s47+7B79z5JrGHeoZ9fIE6ePANv79M45eOLgICzOB90AZcvh+DqlWsIDQ2T0LjmCnwH6SuVGolDURVQ/aaXYtBkwusT30LAufPiPSACyLIGhmxYvmorvvDFb2DJsjWY9/Yy/OznL2HvQW80NbeJTkmriufbaAATwmSrNpY7d2CI88+auxTHqG9CWUUVCotLkZ2Th/BbkbgVES1L3P/dF/8Jn/zMF/DBD31MPPE1Dc1yH84QGU9e8fcJ+kUf2HuQJV0f1Fx04+eGhkacC7qAX//6JXzowx/DB/7kg/jc5/8eH/7zj+NTn/4bCTG0tXWgta0DLa0dwtsHhkzuZFDei3f0uK2+/WPvydfJBbS7Rt1buai4+psA2WbH4SNeWL5qDZhnb2HZVyOckV9YiV/95k0sWLweu/Yexwf+5MM4dPSUeE14L5OFyFfIkj4/dg/VBd/69r/gH/7pG7h0+Zq7soGnTBrv87jI0soF8ybU/GLaBerhVDaY484lmSIiY7Hg7SX4689+Fl/4wpceKchIIOqmvRrD37UHRQlhpdgMX8Hz6UBl//iSVOm4Z9/kqzEY5DdAavn+/o1JqG9SefqMTjNLiz67U34hePanL8qgau004flfvIwLwWFKorCkj4XnqpKopFgijp4ZKx3ZIu2V2cDjEtVmhVLtA7Uofyjjd8tXrAZjZmzMUn5UWaWROK4Hg8CQmxvJLQogSjukqu7ZOIGB01cZ6iByWS5AHLkSVueLKLakQ+58UU0RpApSrO4Yj2vPPj/Lmr+CE7WcLPul2LOBHEEWNVeVC8JZLPQnsnF94GeffR5xdxLlOwHKRsfyoMmCpSu34vcTZ0v0trffgu27DmP9ph2S5MNbkO0RObopxy8dzCx+ST2Uripmg6lZiwqJCrn8XTuidUCWNfAlhPS42iBfeqyNQNLeX3qI9WeeLwAUnyAZqMHPPXgaAcWRo527RJCkrRFBkh+hjEvtWVNeeyLMLp5p3Sf9O00M9zmyVJH6hQCkrUTZoamPe3aFI51L923bvluoRgObSgVnIRLZnb1mvPr6FBw4fErkGN/k3IVrmD13sZSX47vJ5mLeyYCEifju9CEyu4uzOPmeeiAqSlNChc5gHreR+g0YyXmEC6f4GBq3ftfx9uMaxePd4EFvuHL7ECH3bSoN5YH/Dyg2OvXqEfcEHNmzYtFK4BNZUkuqtBxvTZqGufMXSYGvQ4eO4six45i3YBHmL1wquAsMuoqPf+IzuBuvlpfiwazcYoke5+SqcDuJqrGpCUe9vHDypLeweFI9ny1urpHv+hjfx4Ov5+/jskHNloaNZ7Kq4Y2j9/5NGacyaoS/G9/FSUM2eP+f573ezWdF4UquqURJxa6aW9vhc9oXc+e9ja9945/xlx//NCZM+J+Y8McfwN9/6StgtdFlK1fha9/6F3zy01/A7HlLUVXTIFTEQOGy5avxs+d/iZiYOxgy2dDc0ipZtaz3wbQ6NqY2CDA93/MxPw/DV8vosfcTDNmshPJ94YsRFxmi9EGtUcsMvR9xndYqx7x+jPP1dePsZXQbbFkgaPyjbcUEm6LiYuTm5kqmFVMC4hMTkZ6VK0C+HRGJO3fvISk5BekZmaKxUjZxNn11dQ2iY2JQXlEteY5ETEjIVVzgkrXugitqkDwOwN/Luf8HkPWYSBsHGeO+HCNLDHfYVcyJI53ydbymKwt4nke2TY7QP6iMaM/fqDCxiimrkjKXX+elj9u/9/p+Hte/B2SpAN8jU6Z+6EgK08ff5Z5hBheTKzmh3Em25BBk0XNhsppFAeBnApVGsQh9lwvdfX2wOVXwkfOjqbXyPPGUc0kpandcjZvaHpWL/iFcOH8Z0VF3lD1HDZGTZd5lv9/NdROomY++jdASHxD4RmhgzOtH3nfE/dxa6MjzHv077awhwzdoEcQw04oyUoo2GJm6KkwvmiQdvXYrrAx1MHzvtMNkH4LVZYHFxliVFSYrA478o1HNxCBFpdSEA/yDcCM0wr2CrNP66H0dHca8fiy4PHj8MZBFFuG56RzsR+3wgw9XHX3U60c/z1Cs3eXeqKTQRGD8SSv3ZG/i3XCrzw6YjXwRxqiUHFZnyzsSWS4muJBqVZYR5dTpU2dw/RqrbtrEVrHrCe6PPGBHe4ex4PLg8cfQBt+bIvBuyP7/5DWUR+PdX4wjsjuHQ6Yq7d69G4cOHYLFouZKc7CNd4//zt//YJH1OEAkYumlDwgIkLLoWht8FIQ/znPGO/f/R9Y4CgI1S1IQ2SgXJpXQimEq/N+mrP8NI4/CBcQ9QjQAAAAASUVORK5CYII=)
PhysicsFluid-Mechanics
Physics
Capillary tubes of lengths l and 2l are connected in series. Their radii are r and 2r respectively. If stream line flow is maintained and pressure difference across first and second capillary tubes are
respectively, then find the ratio
.
Capillary tubes of lengths l and 2l are connected in series. Their radii are r and 2r respectively. If stream line flow is maintained and pressure difference across first and second capillary tubes are
respectively, then find the ratio
.
PhysicsFluid-Mechanics
Physics
16 cc. of water flows per second through a capillary tube of radius r and length l when connected to a pressure head of h cm of water. If a tube of the same length and radius r/2 is connected to the same pressure head, the quantity of water flowing through this tube per second will be
16 cc. of water flows per second through a capillary tube of radius r and length l when connected to a pressure head of h cm of water. If a tube of the same length and radius r/2 is connected to the same pressure head, the quantity of water flowing through this tube per second will be
PhysicsFluid-Mechanics
Physics
Two capillary tubes PQ and QR are joined at Q. PQ is 16cm long and has diameter 4 mm. QR is 4cm long and has diameter 2mm. The composite tube is held horizontally with the end P connected to a vessel of water giving a constant head of 10cm and the end R is open to atmosphere. The pressure difference across OR is
Two capillary tubes PQ and QR are joined at Q. PQ is 16cm long and has diameter 4 mm. QR is 4cm long and has diameter 2mm. The composite tube is held horizontally with the end P connected to a vessel of water giving a constant head of 10cm and the end R is open to atmosphere. The pressure difference across OR is
PhysicsFluid-Mechanics
Physics
A cubical block of wood of side a and density
in floats in water of density ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAXCAYAAABqBU3hAAABDUlEQVRIDe2T3Q2FIAyFu4tbdAE3aeIovrGFG7CAYxBnOTcVJSDIjcYb7wMmRn5az9cDJbz80Mv6aADNgf90oOs6ENH69n3/00bJHFDBZVmCqMKM4xjmTw6macrbcBiGREODjmtJgLMQ9m4RMcQmu9WJFpo5cMxQcYUoPs5AxMKtmw5GQdhs82JGtlgFUOvP74AKMoxX9wiGQVcsAM4dUOHq2TsDPlRr5doRKHXmwHoxiDDPc7CrBOK02gDgYA2DYztCdn2QAKyXYmu/vQ31m98Bb78I+3ZlrTw6i0hz/2epCA1LAKK8+tBKVH099NvuLQArdMvuEswNAAshwYV2L+mGtRsAIfeRQQNoDnwAbpYC6qEe5IwAAAAASUVORK5CYII=)
The lower surface of the cube just touches the free end of a massless spring of force constant K fixed at the bottom of the Vessel.The weight W put over the block so that it is completely immersed in water without wetting the weight is
A cubical block of wood of side a and density
in floats in water of density ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAXCAYAAABqBU3hAAABDUlEQVRIDe2T3Q2FIAyFu4tbdAE3aeIovrGFG7CAYxBnOTcVJSDIjcYb7wMmRn5az9cDJbz80Mv6aADNgf90oOs6ENH69n3/00bJHFDBZVmCqMKM4xjmTw6macrbcBiGREODjmtJgLMQ9m4RMcQmu9WJFpo5cMxQcYUoPs5AxMKtmw5GQdhs82JGtlgFUOvP74AKMoxX9wiGQVcsAM4dUOHq2TsDPlRr5doRKHXmwHoxiDDPc7CrBOK02gDgYA2DYztCdn2QAKyXYmu/vQ31m98Bb78I+3ZlrTw6i0hz/2epCA1LAKK8+tBKVH099NvuLQArdMvuEswNAAshwYV2L+mGtRsAIfeRQQNoDnwAbpYC6qEe5IwAAAAASUVORK5CYII=)
The lower surface of the cube just touches the free end of a massless spring of force constant K fixed at the bottom of the Vessel.The weight W put over the block so that it is completely immersed in water without wetting the weight is
PhysicsFluid-Mechanics
Physics
A capillary tube of radius r and length l is connected in series with another capillary tube of radius 2 r and length l / 2. If the pressure across the two tubes taken together is P and a liquid flows through it, then the ratio of pressures across the first and second tubes is
A capillary tube of radius r and length l is connected in series with another capillary tube of radius 2 r and length l / 2. If the pressure across the two tubes taken together is P and a liquid flows through it, then the ratio of pressures across the first and second tubes is
PhysicsFluid-Mechanics
Physics
A capillary tube is fitted horizontally near the bottom to the wall of a vessel. If the experiment is conducted with water and a liquid by taking them upto the same level ratio of the rates of flow of water and the liquid is (
of liquid =0.002 Pas, its density =800 Kg m-3
of water =0.001 Pas, its density = 1000 Kg m-3)
A capillary tube is fitted horizontally near the bottom to the wall of a vessel. If the experiment is conducted with water and a liquid by taking them upto the same level ratio of the rates of flow of water and the liquid is (
of liquid =0.002 Pas, its density =800 Kg m-3
of water =0.001 Pas, its density = 1000 Kg m-3)
PhysicsFluid-Mechanics
Physics
The velocity of water in a river is
at the surface. If the river is 2 m deep, the shearing stress between the horizontal layers of water assuming bottom layer at rest
(
for water)
The velocity of water in a river is
at the surface. If the river is 2 m deep, the shearing stress between the horizontal layers of water assuming bottom layer at rest
(
for water)
PhysicsFluid-Mechanics
Physics
A solid cone of height H and base radius H/2 floats in a liquid of density
It is hanging from the ceiling with the help of a string.The force by the fluidon the curved surface of the cone is(P0 = atmospheric pressure)
![](data:image/png;base64,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)
A solid cone of height H and base radius H/2 floats in a liquid of density
It is hanging from the ceiling with the help of a string.The force by the fluidon the curved surface of the cone is(P0 = atmospheric pressure)
![](data:image/png;base64,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)
PhysicsFluid-Mechanics
Physics
A solid uniform ball of volume V floats on the interface of two immiscible liquids (see the figure).The specific gravity of the upper liquid is
and that of lower one is
, and the specific gravity of ball is
The fraction of the volume of the ball in the upper liquid is
![](data:image/png;base64,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)
A solid uniform ball of volume V floats on the interface of two immiscible liquids (see the figure).The specific gravity of the upper liquid is
and that of lower one is
, and the specific gravity of ball is
The fraction of the volume of the ball in the upper liquid is
![](data:image/png;base64,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)
PhysicsFluid-Mechanics
Physics
Work done in splitting a drop of water of 1 mm radius into 64 droplets is (Surface tension of water is 72
10–3J/m2)
Work done in splitting a drop of water of 1 mm radius into 64 droplets is (Surface tension of water is 72
10–3J/m2)
PhysicsFluid-Mechanics
Physics
There is an air bubble of radius R inside a drop of water of radius 3R. Find the ratio of gauge pressure at point B to that at point A.
![](data:image/png;base64,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)
There is an air bubble of radius R inside a drop of water of radius 3R. Find the ratio of gauge pressure at point B to that at point A.
![](data:image/png;base64,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)
PhysicsFluid-Mechanics
Physics
A container has two immiscible liquids of densities
and
. A capillary tube of radius r is inserted in the liquid so that its bottom reaches up to the denser liquid. The denser liquid rises in the capillary and attains a height h from the interface of the liquids, which is equal to the column length of the lighter liquid. Assuming angle of contact to be zero, the surface tension of heavier liquid is
![](data:image/png;base64,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)
A container has two immiscible liquids of densities
and
. A capillary tube of radius r is inserted in the liquid so that its bottom reaches up to the denser liquid. The denser liquid rises in the capillary and attains a height h from the interface of the liquids, which is equal to the column length of the lighter liquid. Assuming angle of contact to be zero, the surface tension of heavier liquid is
![](data:image/png;base64,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)
PhysicsFluid-Mechanics
Physics
An open tank 10 m long and 2 m deep is filled up to 1.5 m height of oil of specific gravity 0.82. The tank is uniformly accelerated along its length from rest to a speed of 20 m/s horizontally. The shortest time in which the speed may be attained without spilling any oil is
An open tank 10 m long and 2 m deep is filled up to 1.5 m height of oil of specific gravity 0.82. The tank is uniformly accelerated along its length from rest to a speed of 20 m/s horizontally. The shortest time in which the speed may be attained without spilling any oil is
PhysicsFluid-Mechanics
Physics
An ideal fluid flows in the pipe as shown in the figure. The pressure in the fluid at the bottom
is the same as it is at the top
. If the velocity of the top
. Then the ratio of areas
is
![](data:image/png;base64,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)
An ideal fluid flows in the pipe as shown in the figure. The pressure in the fluid at the bottom
is the same as it is at the top
. If the velocity of the top
. Then the ratio of areas
is
![](data:image/png;base64,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)
PhysicsFluid-Mechanics