Physics
Fluid-Mechanics
Easy
Question
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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)
The correct answer is: ![](data:image/png;base64,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)
Related Questions to study
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,iVBORw0KGgoAAAANSUhEUgAAALwAAAB8CAYAAADTodofAAAN5ElEQVR4Ae1dv4sUTRA9VETFwMADEQQDAzE6M9noQjMNPJEDQRA21czQzMTgNjP0TzBbQwP/ADE6YQNDQ0PDlrd77+5tb8/s/Oje2+6phqNrurqru1696amZz297x1kxBAaEwM6AfDVXDQFnhDcSDAoBI3yCcB8fH7uvX78msGwm+yJghO+LYGD858+f3atXrwKa5k0Y//fv3+YDrGcjBIzwjWBq1ykG4e/evet+//7dbmLrvRYBI/xaiNp3MMK3x2xTI4zwCZA2wicANZJJI3wkINWMEV7R2C7ZCJ8gHkb4BKBGMmmEjwSkmjHCKxrbJRvhE8Tj48eP7vDwsJfl27dvu1+/fvWyYYNXETDCr2LSu+X169fu+fPnvezs7u6679+/97Jhg1cRMMKvYtK7BYR/8eJFLztG+F7wVQ42wldC011hhO+OXeqRRvgECIPwBwcHvSzbDt8LvsrBRvhKaLorjPDdsUs90gifAGFLaRKAGsmkET4SkGrGdnhFY7tkI3yCeBjhE4AayaQRPhKQasZSGkVju+SNEf7fv3/b5XnC1RjhE4Lb0/RGCP/nzx+3t7fXc6n5DDfCb2+sNkJ4/J87+D94hlIsh9/eSBvhE8TGCJ8A1EgmjfCRgFQzltIoGtslG+ETxMN2+ASgRjJphI8EpJoxwisa3eWnT59G/6kSI3z3eFSOtJSmEppWihQ/VWKEbxWCZp2N8M1wWtfLCL8OoS3RG+HjBMIIHwfH5FYsh48DsRE+Do7JrRjh40BshI+DY3IrltLEgdgIHwfH5FZsh48D8VYTvu6nnX/+/OkuXLjgdnZ2BvP37NmzXlG/efPmYLCq4sXFixcduBOzRPss+fbtW/fly5fg2vD7KpcuXQrqSmzEDv/w4cMV1/b39x3+qorqr1y5MvjfpQFnYv82TxTC45//IkC3bt1yoX/37hMed7SWEq/v3bt3ukOrrypzZ9M2yhrsEvGhn6ir/FMMtH8feZl5HS0dHR3Ndy78+NCnT59WrPiEX+lQWAN2eJ/wIXJrm8qAI0Wwc4M5BQZRCI8dHke04EdEf/z4sYIrCe/fyX7HUvQfPnyYP/HUPyW0yuyjbZDxzuM/ztFeV0rTby3hEQQSPhQQEj6kK7ENN/7169crXVNyhzpBf+3atcEfeVMM4f2dqMRrPdSsCcF9DPSTnK8bynUxhA/taiW1cYcnMVFTpp/apjL1eEIM/VCz4gjvk4DBZp2r3ie8+kOfQiTXNhCefTner0vXh95jfAzaXte/BbWwZjn8GVggvKY01Cih2aa16jWl0T5DkovZ4f2dqcRrEF4JHCJqnV4JXyI+ikeVf9kSHrkojnAZSuEOr4RWmThom8rQK+HZf2h11oRHABHUulKKnjm8+qqEVpl9tA1y6KUV7XWlNH32hK8LVkm6EOHVPyW3tlOuIjz1Q6mLIby/E5V4rS+tTQjuY6Apja8byvW5En46XnxLHk/D+0vdV5qh/dQed3gSEzVloqdtKlMfSmmoG0p9roR3burGO2NXwffaf1pQRXifBH4g4+pnbjIenXw5GbnxZLZCwljz+4SnXSW2yiG9fYd383+PFPs/vtW/BTESqKdjt1O1va/5tzRVhFfzqeXpeOQms8UsM/iyc3Yde24QXlMa2g+RnDrUqteURvsMSU6BQUPCz9xktOPmfJ+O3QiPaI/8bVIaBFbLJq716YT5kKKNTu4AXM9ObgasK8Z6gAfs+LZ8v6v0Gmy/z1CuFQPFrY+8zLwqS7OJGyGdmU3cZDpzDtejiROOdEppqqaL376ajs0mo1PCzybjxc0caWLu8CAmyakyp9E2laFPEWzOm0udAoNGhAc5dsYTNz1J4JUsBK/JDs/gc4xfp9OD8Iv8fT7nbOLGI3kfmS4IH2t+5vDqnxJaZfbRNsihl1a015XS9OdE+JN0hgnw/OV1Nf9tQvi6YKXVLXb4MW5c7Lqj8Wk+P5/3hPCx1hAivNqer6GGvNCHCK82hiCfD+H99GX+8jpZynkBfhvC+zvRJq79HF4Jg/n1lSTGeoAHC+z5NqlDHdJrsP2xQ7lWDBSvPnL9M9IhXT/LdTHR/GUP6Y0m8C0J32fB3cau5vBLdrDDnz7BljSdLrjDk5ghQmubypzQdvg07zFrCc8ArKvb7PC0RULw2q+j6f2n1MlE0ex7C/cJT7USW+WQ3r7DuyRp3bkSnoEurQbhNaWhfyGSU4da9Ske5zpXDnIKDM6F8AislhKvQXglsPpLuU6vwS4RH2KAuso/xUD795GXmdfDUpeUpsd0Wz2UO7wSWmUuXttUhj5FsDlvLnUKDDZKeAS1rpSiZw6vviqhVWYfbYMcemlFe10pTZ894euCVZIuRHj1T8mt7ZSrCE/9UOpiCO/vRCVe60trE4L7GGiwfd1QrhWDWDd5/TOyxSyWw5+BxR2exERNmb20TWXqQykNdUOpiyO8TwI/kLnqfcLTLyW2yiG9fYe37/DkxdbXILymNFxwiOTUoVZ9it1N58pBToHBuaQ0CKyWEq9BeCWw+ku5Tq/BLhEfYoC6yj/FQPv3kZeZ18OS5fBn4HGHV0KrzJ7apjL0KYLNeXOpU2CwUcIjqHWlFD1zePVVCa0y+2gb5NBLK9rrSmn67AlfF6ySdCHCq39Kbm2nXEV46odSF0N4fycq8VpfWpsQ3MdAg+3rhnKtGMS6yeufkQ1mwSFmx8fHp/8DSOjIm2341YIGrkTrwh2exERNmZNom8rUh1Ia6oZSbyXhAf779+/do0eP3OPHj4NHV1YR3ieBH8hc9T7h6ZcSW+WQ3r7Db/F3eB5bube3x9gt1SD8jRs35jcGbo7S/548eeIODw+XMMBFiOTaSfX4teU3b94Uj1UdF8AZcCdm6Z3ScDF1BxPjlO779+/PP7XhMcU/nOuKP177da56nKJ9cHDQiuDEkfXu7q7DX4n4MM7r4vvgwYPgub/EqEsdjfB1R8/jLr169eqcAN++fXP8446Ga5Vz17979869fPny1CcEhv5pkLRNZfS5c+fO6ZjS8GkaX3Bma3d4DaQvY9Gak/rBRX9tU5m2tE3lkvUabPVZ5ZL9x5NAMaCvfepoO3zdIrBoLJ4lFDDqUJt+8VWnKthDwSdrwmOHryqlBRBfaWJ/hwdGVaU0/OhnUYTXIKlMZ7VN5Rz0ILyuWeUc1o816ppV3uT6U/y3iOptg55FqJnSKHAqcwptUzk3vU/43NaP9W4D/kURniTQOgRyjno/paEPbfwLPc7bjOecWuc2PoSB+tNF3ugO7y8wdQD8+dped10fCd91PNaJYPcZDxu5j896h8fiEQAtGhCV2UfbVG6qZ7+m9f7+/lJXnVNldtI2lUOEV/268dD7hG87HjZ0jMpN5t+G8cUQPjX4DGjbmoRPvb6m9vWzpI5RmT5qm8o564tJaUIBYWBQ99WrrS5y3/ljjVfCqx+x7KtNlbfFftaEx+OpqqQGuGrepu1t18eUhvbbjsc4DXaX8Zwbda7jFQP1p4+8nFT3sVQzFjuVT3gNgso0o20qN9WzX9da51SZ9rRNZehBeG1Tucl49NExKg9pfNY5PO5WDZzKMYOIec7K6tmsZ7pVCTk81oXSZ30+4TmT2lTZ9AsEFBPIRRGeQdZaHdZ2yk30Svi2Z7Mq4Tmn1k3mRx8/paGNpuPRP/Q4bzOec2qd2/gQBupPF3ljKY0SkQtNG4DVY270bNbZdOqmejgrFyV11/WR8F3HYwnAq8942Mh9fNY7PBaPAGjRgKjMPtqmcjP9KuF5XtVsijOqZg5PAD3MjJ8lm9lfJpSuL0R41Tex7xO+7XjMoWNUbjL/NowvhvCpwV8EFIQHoXnevHc2Kzp5x1WS8KnX19S+fpbUMSrnQl5ds8p16y8mpQk5TMdR99UvbC12+MqzWcH3yclJyzp5hPn7rp/jlfC6ROq1TeVS9FkTHo+nqpImQKspjc6PHN47eVPVS3Lb9TGloZG24zFOg91lPOdGnet4xUD96SMvJ9V9LNWMPZ/v8NWEn03GbjQeu/F47CZMebz1K0lUZjdtUxl6EF7bVG4yHn10jMpDGp91Do+7VQOncswgYp55qTiblXOFav0smWp9sIti9tf/OFVRhA8RLkQC7ddEf0p4HdhQVsKHhjSZH32qio1fJbli5eOTdUoTIqLvoDoPua/et9f2uu/8Nr4dwf34ZL3DY/EggBYlhMrso20qN9WzX9OanyXZX+dU2fQLBBQTlWPhUwzhU4ATskngm9YkfMiWtqlM29qmsukXCCgmKtfhU0xKE3KYjqPuq1dbXeS+89v4fqkM8cua8Hg8VRU6aPowAkPFpyjCaxBVZsi1TWXTLxBQTFQuCZ+sc3jcrRoYlUsKEvxCMf9W0xrFROWq+BdFeDqpdQgE058hMDR8sk5psHi/DC2A5v8yAuvin/UOj8XDQS3qsMrso20qm36BgGKicin4FEP4EoOjPqlcCvnUJ5VT+ldMShMCjMChNv3qC98Q8cma8Hg8VRUjuBEcHPBLUYRXkqtMp7VNZdMvEFBMVC4Jn6xzeNytGhiVSwoS/EIx/1afWoqJylXxL4rwdFLrEAimP0NgaPhkndJg8X4ZWgDN/2UE1sU/6x3+8uXL88e8nrxMh9GmMvtom8qmX5xmrpioXAo+4EzVLzcs3zrNr1ZfjZuPbdXz6Oho0Meok4RWL27WJjiAM7HLxggfe+FmzxDogoARvgtqNiZbBIzw2YbOFt4FASN8F9RsTLYI/AfA3DU13W03wwAAAABJRU5ErkJggg==)
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
Physics
PhysicsFluid-Mechanics
Physics
Figure shows a capillary tube C dipped in a liquid that wets it. The liquid rises to a point A. If we blow air through the horizontal tube H, what will happen to the liquid column in the capillary, tube?
![](data:image/png;base64,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)
Figure shows a capillary tube C dipped in a liquid that wets it. The liquid rises to a point A. If we blow air through the horizontal tube H, what will happen to the liquid column in the capillary, tube?
![](data:image/png;base64,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)
PhysicsFluid-Mechanics
Physics
PhysicsFluid-Mechanics
Physics
We have two different liquids A and B whose relative densities are 0.75 and 1.0, respectively.
If we dip solid objects P and Q having relative densities 0.6 and 0.9 in these liquids, then
We have two different liquids A and B whose relative densities are 0.75 and 1.0, respectively.
If we dip solid objects P and Q having relative densities 0.6 and 0.9 in these liquids, then
PhysicsFluid-Mechanics
Physics
In a U-tube in which the cross-sectional area of the limb on the left is one-quarter, the limb on the right contains mercury (density 13.6 g/cm3), and the level of mercury in the narrow limb is at a distance of 36 cm from the upper end of the tube. What will be the rise in the level of mercury in the right limb if the left limb is filled to the top with water?
![](data:image/png;base64,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)
In a U-tube in which the cross-sectional area of the limb on the left is one-quarter, the limb on the right contains mercury (density 13.6 g/cm3), and the level of mercury in the narrow limb is at a distance of 36 cm from the upper end of the tube. What will be the rise in the level of mercury in the right limb if the left limb is filled to the top with water?
![](data:image/png;base64,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)
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 fluid on the curved surface of the cone is (
atmospheric pressure)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH8AAAClCAYAAAB1GCJaAAAVpklEQVR4Ae2ddewdRRDHf7i7u7tT3IqUECR4sZZfjV8JEgopUByqtECQ4hBcirR4kALFtVDcNQQSmhD+gfAPsuQzdF72d9y9vbt392RvX3LZu3t7svOdmZ2Znd3rMh34mzlzpunu7jaDBg0ygwcPLnUbMmSIGTp0qKEs+1m0qaenx8yaNaspqHQ15SkFP2TKlCmmq6vL223atGkFUyz+dh0J/meffWbGjRtnxo8fX9o2YcIEM3HiRNOvXz9hsj59+sgx58t67tixY82kSZPMl19+GY9WwWc7EvyCaVD3doCNlhk+fHjdep34ZwDfgRrSCPjDhg1z1Oy8vwP4DszGjBkTwHfQyNu/A/jeQutuWADfTSNvawTwvYXW3bAAvptG3tYI4HsLrbthAXw3jbytEcD3Flp3wwL4bhp5WyOA7y207oYF8N008rZGAN9baN0NC+C7aeRtjQC+t9C6GxbAd9PI2xoBfG+hdTcsgO+mkbc1AvjeQutuWADfTSNvawTwvYXW3bAAvptG3tYI4HsLrbthAXw3jbytEcD3Flp3wwL4bhp5WyOA7y207oYF8N008raG1+Dfd999hu23337zFsBGGuYb+G+88Ya55557ZBp4ly5y8MUXXzRCI2+v9Q38o446SiaeXnnllZT/rXDRrAUBOo1LfAP/mGOOEfCvuuqq/8Cfa665mrYaRAC/tRQYMGCAgD958uQAvgsK3yQ/gO9C3Po/gG8Ro2q7AfyqIW61N4BvEaNquwH8qiFutTeAbxGjarsB/KohbrU3gG8Ro2q7AfyqIW61N4BvEaNquwH8qiFutTeAbxGjarsB/KohbrU3gG8Ro2q7AfyqIW61N4BvEaNquwH8qiFutTeAbxGjarsB/KohbrU3gG8Ro2q7vn1gKeTwZeDgCy+8ULJdyXf34RfAT4niP//8Yw477DABf++99055VXtXC+CnxIeJLIsvvriAv8IKK5gPP/ww5ZXtWy2AnxKbUaNGCfA6q2n06NEpr2zfagH8FNj8/PPPZoMNNjDMZlpwwQXN3HPPbbbcckvz66+/pri6fasE8FNgc/PNN5t55pnHLLTQQsIECyywgGiBxx57LMXV7VslgO/A5o8//jC77757ra/fbrvtzDLLLCPH/fv3d1zd3n/Hgv/999+391s38e1eeOEFARrJ33jjjc32229v1ltvPTm35JJLGj7h3ozf33//bX7//fdCH9Xd3S3t6DVRkwb99ddf5s8//6z0Bg2OPPJIIdBSSy1lttlmG7PttttKf7/ooovK+QsuuMAATJm04v4zZ840xx13nPnll18KwYa2HX300f8H/5FHHjGffvqpee+99yq5zZo1SyR66tSpNfdu3XXXNaj8Pn36SLnKKqsI4TbccEPz4osvmk8++aQUWr3//vvyLqeddpo87/bbb28YG+750Ucfmf3331/uefXVV1N2iUWLIcPqHB988EElN3z4r776ygwfPlyIs/DCC5utttpKJB/wkf5NNtnEzDvvvLKxssXXX38tvn/RNIOpWD4FJgMfAk1gwzvmfRbXItyx4D/00EPm448/Nu+8804lN9o+ffp0s+aaawrBV1ttNenrAV43GEANv759+5p3331XJL9omgHSZZddJu4l4C+77LLmiSeeEMnN+yzeFcbZd999pX29JL/K4EMYCK5x/Pnmm89sscUWNam3wV9//fWFePPPP7+ZMmVKQ4DEAUn3Q9e7xx57yHM0wDRixAjz+eefC8PFXec6F8BP0Gr0h6jZzTffXAhOKBcpV9C1xPijK6BLAJRjjz1WAHERPsv/GN533nmnWWKJJXqBT5fz0ksvierPcj+tG8BPAJ8+9tprr5WgDpG8jTbaKBZ8mAADcI011hBg1l57bTNjxozcgCgwWiL1dD9DhgzpBTyMRqTx8ssvFw0FkHpN2jKAHwM+RMEY2meffYTguHeAjJSrxNslGmHTTTc1dA0Awng/hmJaEOrV4z2effZZo16FqnwtCTxpt1DvPnH/BfBjwEfNsggloAPmOuusU3PvbNDtfaQfIwxQMPzefvttQ9cRR/Qs59BA559//v+kXsEnznD//ffnsjMC+BHwkSII3tPTIwRfZJFFzNZbb50o9coASL8afgz6wDyNekq8CwBhUyjYceXAgQNz2RkB/Aj4qNlnnnnGrLzyykLw1Vdf3Sn1MABdAkwCswDQ4MGDhYmySHm0Lhrouuuuk4GkOND1HHYG70zAJnqPescB/Aj4uHeEaiGsundxVr5KvF1STw0/YgKMB+BH1wMg6T+kHjAPPvjgXlK/2GKLybGGlZUBzjvvPAn6AGjSPaPnA/gW+PjSb731lvjzEHXFFVdMtPBt0HUf8DfbbDNhGjwEEj3I/IkSPc0xXQ+LITN8jBvZr18/w/KoGpDBpZw4caI8jwgjLiluXxY7I4BvgU+4lJEtgjXq3mkcXwF2lTDAcsstJ9KJ4QfQWQChvoIyadIkc9BBBwkTcA+6gUMPPVTufcopp5hvvvnGvPnmm8IUeCYPPPBAJk2jz1GGqmyED6mHwPvtt58Qd+mll84k9coUMAtDvXgJMNGtt94qoKWRdrsOo3cEmdAAqH9sEcCCGdBKJ5xwgpynW6EO7w4j2Pdw7Qfw50g+BCQ0q30pAGaVehhAYwFq+HV3dwtw9OEuMKL/q7XPeZgzCr4yBP/bdaP3SToO4M9Rs7hljJMjVfSxadw7lfZoaRt+K620knnuuecyqeM4sFzgx13jOhfAn9MnA5BG0XDvADAKatpjrsUAw1uAmc4999xcqt8GL4BvGWc2YRrZp2/FIj/nnHMEKADDYm8EfFQ/1zMYBPg77rijqGwAzPuuAfwSwMdgwlBCqgEK9y5PXx/VCtzDTvO+5ZZbckXhlFkC+CWAz3g4/jOuHRY6yZmNSL0ygRp+GpRpxPCDAdKCTz+O8WdvSecq3edDUIikaUwM5BQBvDIA99IsIDQKIVgsdJXmLGUa8AETLYaLqNb/66+/LseUPI/z/E+9SoOP/0xgRBMxcO+KBB/ptw0/In64lFlA17ppwCc0TZBql112kZFIkk2JWxAJJDhEN8QI5c4772yuueYaGXiCGSsZ5CGip0kSMACjZ0WDDwMsv/zyYk+wj4GJ9Cmoacs04HMvbJg5n0iTbowkXBiOEu2DXXPxxReLBqqs5CP1JEng1kEQBmSKMPRU5Wuphh/PYHrX9ddfn8vwSws+QN92223SJgJWMNrs2bMlv4BsJN6DDCXqVRZ8pP7ss88WYhCGRT0XKfUKPtJOwEindTP5A8Jnlf604BOswrMAZNp16qmnmosuusgwFoAGYsYRMXzqVRJ8VONrr70moViIVJR7p4BHS6Rfh3oZ9Hn88cczJ3rkBf/EE08UJmcsgGdXHnwkD9WHa1ekexcFXY+RfqZyI4kwG2PvKnlF9/m25KP2uT9Tyxmq1gkflZV8VB0EiiZnKlBllXQpxPkBn/x/DD+kuUjwuSdxi7vuukuew+ASGo6h35dffrmWZnbjjTdKvcqpfaSehEftg/OO3mVlElQ/BheahhDyDTfcICnXRYIPM5E9RD8Pk7Fh+TOHEGnXkUa6AM5Rny6wEq4enE5CxKBBg4QwqEV77l1WQLPUR/VTXydeHHLIIZny7dP0+TA2OX/cWzdm4DLNi5xCPUeJ14EGrIyfj3v39NNP16JuaZMzs4Bcry5z+jXixwgihh+ApZH+NOCj9gGTgSomjLLRDdBuSuYScI7/kXieWwnJR+ohNMYW6lDdO5XIeqAV9R/Por9Xw4+hXqJyvJuLAdKA77pH9P/K9PkQD8mA+ICPe1eGX+9iFPp+HerlXYizp8nxC+A3MKqHhGH04OdidDHJsRXg80xGDnkHRhKxvOl7o1IZPQ7g5wSfaBp9IStmIvW6tEozVb5qBJ5JxE8NPwZeAN+l+gP4OcFH6u+9914BHfDtpVUUlGaWGH5rrbWWMCLz+x5++GGn4RfAzwE+Uo9kDRs2TIiNr9tIcmYRTILqp79nQgbMOHLkyFrQJaru9TiAnwN81D3JmVnn3hUBcr17YPhpxI9BJSJw6n4BuEYA8VBg4HrgYzBSz9V1KCNp6b21j8rX5EymNSFxrejro4yA9GN0Yvgh/ZpcYQNDV8WqWzAF/jkg25M2CFjhu5OlgzH75JNPZgoZew0+0kK6Etm4ELhV7l0UePsY45N3O+CAA3oZfkgykTmikPwHuGiDww8/XOoTwsVNZO7+TjvtZJgYiu2AplMGcpVeg09Ui9g2QRXcqqKSM23wGtlH9ZNWBfis6MW6h0TjAA1pZ1CG0UD+pw1oLNrAMV2FrgfAMRM3sW2y5Al4Cz5Sz6aDFq1075IYRA0/FnMAQBIuSDJRiWX/jDPOqHUN1InbyBAmewdm12vTlN6Cj9qMJmciaUlAtOp81PB79dVXa6ob6a+3Ho8yAku0UTeL1MMcXoJPo1CBdnIm4LaDoRdlMjX8dN4AfTtGqkouTMy3fBToaInBOGHChFzTwbwEXyVG3TtSqCBylPDtcgxTsnI3wBKFpLtSKYaJWaRBu4Yo+ASssA3SjA8oQ2npJfj0fc1IziyKeWBMNfzov22rHVCx8lnoIQo8xyeddJIYicosCmya0jvwIRZ+r65gxQhaO/b1NuNEDb/jjz++1zp+GH7k2hOnsBmABSRYIpeuIQ3Y0TregQ+hCJhAKEbwSJ1qd/BhBN5x1VVXFXB1+Xa6LwCjJD2LGTc2+AR88hh6ygRega99pe3etXNfH5V+In4wLMYfy6rabh9dGbl3Cj42AKlYRPkUzKylV+ATICE5s6y5dzZYZezDqKhyAGaol34chgZUInfYApp4SpBH4/9ZQdf6XoGPi6TJmRAJK5rhU1RqJ2ws4oDKx32DgadNm1aL+MEEbAceeKAwB2sF0tcDoIKZtfQGfKSeKdDEuJEcXCeSJXHzOmXjfUkqRe3TBr7wYfv8qHjC1biwjX5oAUbxAnwaQZ9IeFT7RB9KMnwx9NSHpyTix/f9mIGTx72ztYMX4EMEVrnG52Vu+m677ebFttdee0mARwd7AI62YuEDnA1knn0vwKfhGD8M3yIRaTaYRbc09Rupk/c52p48wKa5xhvwaSxSgWpU4yiu5H9CpiRBIFEQwHVN3H3SntN34nkYaEhtlucVIeFJjOAV+EmN5DxgQXyAZ4Fi8uZOP/10YRgAqndt3v+UuBhpLPBIpg0Mx3vAAHnvW9R1+n4aF2FQqfZdPR++rgWRCZYA/oMPPmgInapHwFh5I0GSNCBgrWOgEZRhfjwjdKRm0RXwXmiCNPcpo46X4CPJBEUAljg/0TJW3NLgD54ALtUrr7xSugTyLkg7S6arB0IUj2/j8Nk2ZsvCINSBQcsAOemeXoEP8XD5kCZU7Jlnnln74qUSXktU/rffflvrCugOytq+++47c9NNN8UOy/KVjKFDh4pWAoxmagMvwKcRgI6UMf2JfDb9yqWCbZcMm9K/ESghilb2Rm4e39xh7N1+D3ufxZpI1CRpk2wemKAsW0Q1QceDD4HIeT/rrLNkMoYudmwTNrqv/S99MDNmmrGxGBKZuNF3iTtmJBID8amnniq1K+h48DHoUPGscqXZMHEEtc8BPtLP7J1mbQCvK2PY7xK3jxbYc889a1/YUEktuux48CGIGlUsdkA/r4kccYTlHFLImD8jgKxfU/ZGGhYTMHR6eNJ7MX8Pb4T62C1lG4BegK8SgcVMX4kVz/Ik+K9xfb8mPbJQEZY2fneZG88hk1iHY23w0QiMPJKpQ9ye92EDGG1XWaVX4CuRcPMAE+mZOnWqfCAxmgXDZAgaX7Z08U4wJGvj2KAzMte/f39ZMJH34H1h3maArnTyEny7cbhvrEGDVJHizKLDOjv2kksuESnT+mWUPB8GROpJLeObu6NGjTKPPvpoTcrLtuqT2uU1+HajkSrUKeeIsLEOH6tToh2SpI3BIo0QEptnw6VEs3AvjnWBI85R334m+4APkzHaSJiXoJN2MUnPjd6jrOPKgA8BaSxqXoM5RNcYrYsDgXMACqOwdBnJkmyo7yuuuEK6Ej3HVy8vvfRSuW8UKBiCMXmeC8PATHHPi17XjGPeA+b3NrafREQa7urvUccEXPAgtL8eM2aMxBWw3nVpFWYGsQYAwMY9j+e0SrXHvY+eqyz4SgBXyfiAftYUy5yo4E8//STqn/4bpiBaiFEXp/Zd92/l/wF8x2ofdBHMgGVQCENx/PjxEoenO9B1dRg4oh9vJZB5nh3ATwk+Uo+1zugc0UQ+W6ILK2ADBPAdhMzDna2+RiUfqYcB+FwJah/jjUkWqP0g+R4CD+Mh0XfccYeofMAnUkf/zn+6SgafZlM3stXMmuX5Qe07mBZ3b056k0g5nzCBIQgh6+dXWc+3nVy4tAwQwE8AH8IAPGDvuuuu8ll0xuMJDuHTDxgwQCaBcm6HHXaQ6GGn9fsB/ATwVXo0ZRvJZtNj0qrx3zlHPh7n9ZpOKQP4DvAJzmhEUEtCxbqvJZGy4Oc7iNkpUsF7ItWEgMn3I4pHrl104zwb6WMwRSe1L0h+HWalz+fLHPTppHqxiGN0Y+UP0sEIAZedBl40YxUCPjfB1WGEi5EuVGHRL9qq+6HKmeRB7P75559P3Bitgw6tes88z20YfPpE1CPfqSNrtqenR1KW6APzvFC7XQOBaB9agDbB2OQHsGHdc47/XINE7dYu3qch8LkYYowbN05WkGYSAq4QqpDZPhClHRud553QAGrUkYrNhpWv5/Lcs9XXNAQ+DWesmjw5ZqD88MMP4gMT8mSl606MeiUBgvQzvMvYvg7vHnHEETK8y39J17Xz+YbAR+qZZAAxyJsn5k2+OcckJHZa0CMJKIiEFiO4Q/YPHybWtfJpN3ZO0rXtfL4h8ElpIrOFPHOSG5AAhjlZVGj69Oly3M6NT/tuEAmDjrw72vjjjz9KijVMzmogGLpp79VO9XKDj4HDxSQ0MLTJaNfJJ58sUs9iQc3ORG0GUbXNzPEbOHCgfBb17rvv7ljvJjf4qHymPDMBgulF5LMxWYLhTVRkO6YtFcEgMDXTw0gFp4vrZCbPDT6uDlmprBw1duxYsXq5GcTwFXgkn/YR0WOePTZNJ9s1ucCHCGw65xyVjybwFXQ0BoQC6NGjR0u7yeXDrpk8ebKZMWNGdfx8gMft4cvMrBWHD+w78HRleDD6QSR190jn6lTGzyX5KgnEsrH4uUkR/Wm73oP2sbHAAoEspJ+SDbuHrqBd373ee9UFX7/0qI2veqnjF7h2uiH1ELgTaYO2RqPFTtqgXyOAQYWw+UcDGBfNzXpFdGO9VuMiVWnEiBGysiWrW4bNLxoQlyFIpZ9oq4GvBk0o4z9n5iNdmEjaFc1WCcf/z+DxjSYMx5Ov8C/cNtAdudPAbQAAAABJRU5ErkJggg==)
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 fluid on the curved surface of the cone is (
atmospheric pressure)
![](data:image/png;base64,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)
PhysicsFluid-Mechanics
Physics
The minimum horizontal acceleration of the container, so that the pressure at point . A of the container becomes atmospheric is (the tank is of sufficient height)
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)
The minimum horizontal acceleration of the container, so that the pressure at point . A of the container becomes atmospheric is (the tank is of sufficient height)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANQAAACgCAYAAAB0bULPAAAS/0lEQVR4Ae2dC3AURRrHE8xjNyE8AgkEUEgw5MU9iOCJhV5pwWmVKAgYXh6JYFGKqIggInoi3FkEH6CnyCMgIqiIWIgiEEQMFo9wByGc4PHIERDDm/BMBIHv6utj5za9s9kdtjeZnflP1VSmZ3p6p389v8xMT093GJloKisro7y8PBo/fjxVVVWZ6MhwKHVNoKioiPr3708zZsyo658O6PfCAtpb8c6bNm2isLAwSklJocrKSsWpI7lQIjBz5kxxLvTt2zeUDptMJVRxcTGFh4dTRkYGnT59OqRA4mDVEpgzZ44QasCAAWoTDnJqECrIgJH89RGAUNfHrcZeuELVwGHrAIRSUPwQSgFEiyQBoRQUJIRSANEiSUAoBQUJoRRAtEgSEEpBQUIoBRAtkgSEUlCQEEoBRIskAaEUFCSEUgDRIklAKAUFCaEUQLRIEhBKQUFCKAUQLZIEhFJQkBBKAUSLJAGhFBQkhFIA0SJJQCgFBQmhFEC0SBIQSkFBQigFEC2SBIRSUJAQSgFEiyQBoRQUJIRSANEiSUAoBQUJoRRAtEgSEEpBQUIoBRAtkgSEUlCQEEoBRIskAaEUFCSEUgDRIknYXqjy8nIqKSnxaz5x4oRusUMoXSy2XGl7oXr16iV6qeFuwHzN3vpag1C2dEc307YXavTo0dShQwdtTktLo4TEFqJLMPf1vLxkyRJdiBBKF4stV9peKLnUi4u3ULc7/0g/V1TIm7yGIZRXNLbbAKGkIn9hwosU7Yyh9+fPl7Z4D0Io72zstgVCuZV4RcVhSs/MoiiHk7r3+BNVV1e7bfW+CKG8s7HbFgjlVuLz539AkdEOMTtjG9K674rctnpfhFDe2dhtC4S6VuK//vqruCq5hOK/eUOH+XU+QCi/MNkiEoS6VszffruOHDGx4uoUERUt/t54Uzvau3evzxMBQvlEZJsIEIqIrly5QkPy8ijS4SSHM4ZiG8aJv3yVemXSZJ8nA4Tyicg2ESAUEf3rXz9Q+9RU+nNuHt1zzz3kiI6mXr16U88HelF25y507PjxWk8IFopfCnfs2LHWeNhofQKLFi3CcDb//vduWr/+e3GlGjNmjAAyffp0unjxIq39dh0dPXq01jOBhYqIiKAbb7yRPvvsM1q5ciVmmzJ4+umnxfkzcODAWs8Zs20M2vhQTz75pACSn5/vd55ZqNjYWLGfr+ZL2O67iZcVGA0ePNjv88cMEYMu1JQpU/zOJwvlcDgoJiaGunbtSnfccQdmmzJITU0V/1gHDRrk9/ljhoimE4qHBM3KyqJLly6ZgQ+OoZ4ILFiwQAiFIUGvFYDrls/oFco1xu6ZM2fqqSjxs2YgUFBQAKHcCyJQoTBotTtN+y2j2lwqcwglAUHQEAEIJeGCUBIQBA0RgFASLgglAUHQEAEIJeGCUBIQBA0RgFASLgglAUHQEAEIJeGCUBIQBA0RgFASLgglAUHQEAEIJeGCUBIQBA0RgFASLgglAUHQEAEIJeGCUBIQBA0RgFASLgglAUHQEAEIJeGCUBIQBA0RgFASLgglAUHQEAEIJeGCUBIQBA0RgFASLgglAUHQEAEIJeGCUBIQBA0RgFASLgglAUHQEAEIJeGCUBIQBA0RgFASLgglAUHQEIGQFurHH3+knJwcuvXWW2nSpEl04cIFQ5nXiwyh9Khgnb8EQlaokydPEp/83KFgs2bNRE8zEyZMEL2/+pt5vXgQSo8K1vlLIGSF+umnn2jHjh0in6tWraIGDRpQp06d6Pz583Ts2DE6dOgQsXRnz56lsrIyOn6tf3LeduDAAaqqqtJlBKF0sWClnwTMJhQPhOHPVKOjS5aH+xbnEd2vXr1KixcvpsTERGrbti1NmzaNevfuTa1bt6axY8eKODwA9V133UUnTpzw+C0I5YEEKwwQMJtQ365bR++//77uue6erRpCLVy4kKKiomjFihUizrlz54RALBlfxfgKxv1lJyQkUFFREeXl5Ynw0qVL3dMUyxDKAwlWGCBgNqF4ZJn45gnU+dY/0KtTptDefft0c6MJxRUR2dnZNHz4cC0i997KI2HEx8cTy7V69WohkGtEhEcffVSEP/roI20f1wKEcpHA3+sh4E2oy5cvizGbf/nlF6qrmUeP4Vu+h4fkakPdJrZMosceH0F85eJjck2aUOPHj6fc3FzXeuKhPbn3VpdQp06d8hBq6NChQii+NZQnCCUTQdgIAW9CvfPOO9StW7c6HUTizjvvFI82v//d7yja4dSk4oEEebTOu7t3p6mvvU7nz18gIdTcuXPFcxLfI3799dfE/ZH/8MMPYlynVq1aiREx+Aq2du1aIZCrA3eXUEuWLPFgBaE8kGCFAQLehBo5cqQ4B+tjqJ7IyAhyOmMo4tqA7GIcaYeT4ho3oYdyBtDBgwcprLS0lJKSkog76XcdJEvEtXzLli2jJk2aUGRkJE2ePJn4Fo+XuTKCJeTaQA7zLSDXBLpPEMqdBpaNEvAm1K5du8R5yc/5dTkXFhZSv4dyKDL6/1eo9MwsmjRpMm3fXqplL6yyspL27NlD+/fv1+YjR46ICBUVFaKqvLy8nHbv3i3iuZa5Cp0HouYw/+X7TPcJQrnTwLJRAt6EMpqOqvj8eqhtcgrFxjWiHn+6hxYuWkTHj3vWbmvPUKp+2JUOhHKRwN/rIWA2oZYu/Zxy8x6hr1eurDU7EKpWPNhYXwTqQqiSkhJas2YN7dy502c2/R1eCUL5RIkI9UEgmEJVV1fTxIkTacSIEfTggw9SXFwczZs3T0k2IZQSjEhENYFgCrVx40ZRAffcc8+JOgKujOMKNn6vFegEoQIliP2DQiCYQnFTufz8fJo6dSq98sorQq5bbrnFa7tUIxmEUEZoIW6dEQimUNxoYfr06dSvXz9x63fDDTeIT5f4VjDQCUIFShD7B4VAMIXilj18m9enTx+tsUJmZqaS7wAhVFBOByQaKIFgCrVhwwZKS0sTH9Xyi+L777+f0tPTacuWLYEe9v+aHgWcik4CeA+lAwWr/CYQTKH4ILghgvstHjetkxsn+H2wbhFxhXKDgUXzEAi2UMHKKYQKFlmkGxABCCXhwy2fBARBQwQglIQLQklAEDREAEJJuCCUBARBQwQglIQLQklAEDREAEJJuCCUBARBQwQglIQLQklAEDREAEJJuCCUBARBQwQglIQLQklAEDREAEJJuCCUBARBQwQglIQLQklAEDREAEJJuCCUBARBQwQglIQLQklAEDREAEJJuCCUBARBQwQglIQLQklAEDREAEJJuCCUBARBQwQglIQLQklAEDREAEJJuCCUBARBQwQglIQLQklAEDREAEIR0alTlVpngaNGjRJdNb3xxhsCZOXp02IUxNqoFhcXi2F1MjIyxGBvtcXFNmsTgFBEtHHjJrqv5/30yeJP6ZFHHhFyjB49mmbPKaDeffpS2X/+U+tZAKFqxWOrjRCKr1CVlZTduTNFOWMoPr4ZNWzYkJo0bSqGUOz7UE6NsUj1zg4IpUfFnusg1LVynzV7do0xSHnYRB6kanVhoc8zA0L5RGSbCBDqWlGfOHGSktvfXEOqP951t8+rE+8OoWzji8+MQig3RH95eWINoeZ/8IHbVu+LEMo7G7ttgVBuJV5auoPimycIqVI7pNHRo0fdtnpfhFDe2dhtC4SSSjxv6DCKcjjpr3/9m7TFexBCeWdjty22F+rkyZNiNHgeEZ5HiJ82fToltW5Diz/9lPbt26dt4+0cPn/+vMc5AqE8kNh2he2FevHFF8WLXB53h2cexCra4RDvolzrXH/Dw8Np+fLlHicLhPJAYtsVthfqtddeo6SkJG1u1aoV3XTTTcR/3dfzctu2bcXo2/LZAqFkIvYN214oHmaRB/31d75y5YrH2QKhPJDYdoXthVJR8hBKBUVrpAGhFJQjhFIA0SJJQCgFBQmhFEC0SBIQSkFBQigFEC2SBIRSUJAQSgFEkyVx7tw5ev311+nAgQOGjgxCGcKlHxlC6XMJ5bVr164V7yXnzZtnKBsQyhAu/cgQSp9LKK99+OGHhVDdu3c3lA0IZQiXfmQIpc8lVNeWlpYSC+V0OikqKoo2bNjgd1YglN+ovEeEUN7ZhOKW9957jwoLC0V3CNzsjDvu8XeCUP6SqiUehKoFTohtOnToEE2dOlUc9fr16ykyMpKSk5Pp559/9isnEMovTLVHglC18wmlrR9//DHddttt9NJLL9Fjjz0mbvn4KsWi+DNBKH8o+YgDoXwACpHNVVVVxL1dffPNN7RixQrxd8KECaJyomvXrnTp0iWfOYFQPhH5jgChfDMye4zt27fTvffeS6mpqbRs2TJxuBcvXqRnn31WCMVXqQceeIB27dqlZaW6utrjq24IpeG5/gUIdf3szLJneXk5ffXVV6Iy4vvvvxeHdfbsWREuKiqi7777jr788kviZ6yrV6/SJ598Qp06daL09HTq27ev+BCVd4JQCkoUQimAGEJJbNmyhRo3bqxdufjq1bNnT+JPe+bPny/WDxgwIIRyRBRmpqOFUGYqjeAfC3+UyhK5zw0aNCDuTmHRokUQKtAigFCBEgyt/T/88MMaMrFYbdq0oQsXLpBrG65QAZQphAoAXgjuevr0aerRo4cmVUREBL355psiJwUFBbhCBVqmECpQgqG3P0v19ttv0zPPPENffPGFqKjgXKBSQkFZuoTKysryq+tmBT+JJExKALd8CgqGheLux9q1a0dcxbpt2zbaunUrZosz4HJ2zVzeJSUlooUFP1MNHDhQwZlVd0mYqpZv06ZN2v00i8X31Jjtx4Db/blq/vr161d3Nij4JVMJtWPHDu0l380330zt27fHbFMGHTp0EC97x44dq+A0r7skTCUUt/E6fvw4HTt2DDMY0JEjR4hbWYTSZCqhQgkcjhUE9AjYSqgzZ87QwoULiT8t0BusQA+Q3ddxmztuMb579267o/Ar/7YSik+KmJgYat68ueFeePyiacFIM2fOJIfDQU888YQFc6c+S7YSas+ePRQbG0sJCQl08OBBXZr8Lc/m4mK/vtnRTSCEVnJ/9FwRxFdub9O0adNEjVtubq63KFjvRsB2QjVq1IhatmzpIdThI0do9pw5lN25Cz03bpxo8ezGyZKL3Kp74qRJ9PvsW0TeD+l8ns6tGLgKe9iwYZZkoDpTthSKh9ThFs088dXo+fEvUGpauhjClEes59567DLt3LmTOM+R0Q5qm5wiWGzavFnL/owZMyCURsP3gu2Eatq0KbVu3YZmzZpNAwcPpsSWSRQZ7dQG2W6XnEKPP/64eGYYMWIEWXnm56KRI0dScnKKln9mwUwe7NOHVq1aTa+++qoYNA9XKN8ycQzbCcUDwDVu1EiM/xvp+L9I/B/a4YwhZ0yM9pbe9bbeyn/Dw8LEcyXn333m8ZGdsQ0pq+NvRGsVCAWhPAhwpQRfoVq2aCGeGQYMGkxN4ptpJxKfRBkZmZQ/ZYroAis/P5+sPHM3X9zveEZGhsaApWImffo9RIVrvqG/vPwybvk8ziTvK2x3hYqLixPDlFZWVopPBbZu20bPjhkr/hPzyRTfPIG4oxG7THv27KX4Zs3FbW9aegaNemY0/eOf/9QqZbjaHJUS/p8NthPKWy0fdy4yp6BA1PKNCbH2Y/4Xt2fMF16YQB1/+1t6++9/p3379nlEQC2fB5JaV0AoCQ+/k9m6dRtx11dWn7jt5M6du7QaT738Qig9Kt7XQSjvbJRv4Srq4cOH05AhQ0SfCdyNltknCGWshGwlFDc9io6OFhUTRgcAM4bVMzZ/ODdo0CDq0qWLVou4dOlSz4gmW+PqmSjUPvSrL4y2Emr//v2UnZ1Nt99+O1VUVNQpc35ZzJ8j8MT9J4SHh4tGuhzm5k7caoEnvtXknlRdEy9zE6H6mvjLaX4vxw2KMfkmYCuhLl++LL6z4m+ueLmuJx4ek9vGpaWlUU5OjtYhCb885g8quedUrlXj/r95+1tvvUU8UBlXa/NyKNwi1jVTs/2erYSqb/h8m8m3TlwNzQ10uTNHnrjrYl7Hoh0+fFgbT6lbt26i2+IWLVqIqn7ehsncBCBUPZTPggULiHtIzczMFL/Ot1UslKv/hFGjRokwf7vFt4DcFUBiYqLW73c9HDJ+0k8CEMpPUKqj3XfffaKXVE6XO9BnoXr37i1+5qmnnhLhxYsXE98mpqSkiBbyZWVlqg8D6SkmAKEUA9VLjp/Xhg4dSs8//7z2HMRdDI8bN05E57FnWSge5oUnHluJw59//rl41mOh+LbP39H/9I4B6+qGAISqA85cU8dV5iwJVzy8++67oq2g68M+1xWJG+7yc5Wrar1///40d+5cMZwm7ztr1qw6OFr8RCAEIFQg9Azsy7338K3d8uXLPUZD5zFo+Tlq3bp1xGMq8V8Or1mzhjZv3izCvC93BonJ3AQglLnLB0cXYgQgVIgVGA7X3AQglLnLB0cXYgQgVIgVGA7X3AT+C+ZnStCQ2GlzAAAAAElFTkSuQmCC)
PhysicsFluid-Mechanics
Physics
A tank is filled up to a height 2 H with a liquid and is placed on a platform of height H from the ground.
The distance x from the ground where a small hole is punched to get the maximum range R is
![](data:image/png;base64,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)
A tank is filled up to a height 2 H with a liquid and is placed on a platform of height H from the ground.
The distance x from the ground where a small hole is punched to get the maximum range R is
![](data:image/png;base64,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)
PhysicsFluid-Mechanics
Physics
A cylinder containing water up to a height of 25 cm has a hole of cross-section
in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out?
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)
A cylinder containing water up to a height of 25 cm has a hole of cross-section
in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out?
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)
PhysicsFluid-Mechanics