Chemistry-
General
Easy
Question
Consider the given figure showing that possible levels of the energy of
ion depending on internuclear distance versus potential energy of the system .
![](data:image/png;base64,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)
It may be easily assumed that the ground state of the molecular hydrogen ion,
corresponds to the lowest level which means that
- Curve 1 represents the most stable state of the system for
ion
- Curve 2 represent the most stable state of the system for
ion
- Curve 1 indicates that the molecular hydrogen ion is formed
- Curve 2 represents the energy level of the antibonding region.
The correct answer is: Curve 2 represent the most stable state of the system for
ion
Related Questions to study
chemistry-
Which bond angle
would result in the maximum dipole moment for the triatomic molecule XY2 as shown below.
![](data:image/png;base64,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)
Which bond angle
would result in the maximum dipole moment for the triatomic molecule XY2 as shown below.
![](data:image/png;base64,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)
chemistry-General
physics-
A long rubber tube having mass 0.9kg is fastened to a fixed support and the free end of the tube is attached to a chord which passes over a pulley and supports an object, with a mass of 5kg as shown in figure. If the tube is struck by a transverse blow at one end, the time required for the pulse to reach the other end is
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)
A long rubber tube having mass 0.9kg is fastened to a fixed support and the free end of the tube is attached to a chord which passes over a pulley and supports an object, with a mass of 5kg as shown in figure. If the tube is struck by a transverse blow at one end, the time required for the pulse to reach the other end is
![](data:image/png;base64,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)
physics-General
physics-
A plane progressive wave is shown in the adjoining phase diagram. The wave equation of this wave, if its position is shown at t=0, is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAP0AAACnCAYAAADaIFptAAAgAElEQVR4nO2dd5wVRbbHf3375jARhjwSFRCRpLiigIQl6YIMwUAwgMvDNYDsM+zqgwVBFFbUhwjmtGICURRRFGTBFTNBURCBQZgZZoaZmzvX+wNO0cMKLnAn8G59P5/7gZnp213dXafOqXNOnZIYYwwCgSBtcNR2AwQCQc0ihF4gSDOE0AsEaYYQeoEgzajTQm+aJsLhMOLxOCzLgq7rsCwLkUgEqqoCAP+baZpQVRWGYaS8HYlEApqmwbIsqKrK26GqKhhjMAwDmqbBNE1YloVkMgnLsvhHURQwxmBZVrW0TyA4Geq00EuSBJfLBZfLBUmSUFZWhvLycni9XjgcDpimCYfDgWQyyY83TTOlbVBVFbIsIxwOw+FwwO12c+F2OBwwDAOGYcDhcPCBgQSdME2TC7vDUacfuSANqNM90DRN+Hw+OJ1OWJaFrKwsMMYwadIkSJIExhgfABhjfJBIJTTo+P1+6LoOwzDgdrvhcDjgdDoRDochSRJ0XQcAyLKM66+/Hh6Phwu71+uFJEnQNE0IvaDWqfM9MJlMIhqNIhqNwrIs9OvXDwsXLoRhGGCM4dtvv4UkSVU+qUSSJHz11VcwTROMMciyzC0Ky7KQk5NT5ZqapqG4uBg7duyAZVm83TRICQS1TZ0RetKUNO8lAQOAjIwMZGVlYevWrejWrRs8Hg/cbjdUVcX777+PeDwOTdOg6zo0TYOiKFV8AAC40JL2peuR2U1+AfpYlgVN06BpGp588kns3bsXDoeDz+UdDkeVOb3T6eTnfPrppzFz5kzouo5gMMiFXmh5QV1Anj59+vTabADNgf/3f/8Xe/bsgWEYePnll9GoUSPk5ORwc12SJIwfPx6PP/44QqEQTNPE2rVrUV5ejvPOOw9PPfUUFEVBfn4+3n77bXz88cfo0qULF3LGGJ566il89913aN++PTZu3AhJkuDxePDoo4+ivLwcLVq0wLJly/D+++9j9+7dsCwLr732Gj766COUlZXh+++/R3FxMQ4dOoQVK1agVatWSCaTeOqpp/Dpp5+iadOmyMrKQjKZxK5duxAMBpGfn88HMNL0QvgFtUmt9z5d1xGLxeDz+fDEE0/A4XBg1apV2LNnz3G/Q8Lj8Xjw/PPPIxaLIRqN4u2338bSpUtRWlqKBQsWwO12cy1rmia8Xi+ef/55fPXVV/jkk0/wyCOPYMqUKYhGo3jttdewYsUKFBYWIiMjAwsWLEAgEMDGjRvRtWtXdOzYEYWFhVi6dCnWrl2L3bt3w+v1Yvr06cjJycEXX3yB7777Dm63G3l5eejUqRM++OADMMbgdDphmiacTmfKpx8CwclS60LvcrngdDpxxRVXQJIkdOjQAeecc85vfo8xhu+//x5Tp05Fo0aN0K1bN7z99tuoqKjA8OHDkZubi1gsBq/XC1mW4XQ6UVBQgG+//RZLly7FDTfcgJ9//hmDBg3CH/7wB6xevRrbt2/H+PHjcd1116FBgwZo3rw52rVrhz59+mD06NG4/vrr8fXXX0NRFNx9992YOnUqrr32WowaNQpt27ZFIpHg0wpJkhAIBOBwOCBJEvfoCy0vqG1qvQdKkgSfzwdVVWGaJhYvXowLLrgAF1988XG/o+s6EokEdu7ciSZNmsDr9SInJwe9e/fGhAkT0KBBAyiKgkAgwKcPhmFAkiS0bNkSc+fORVZWFnw+Hzp27Ijy8nIcOnQIuq7j4MGDGDFiBB5//HEuoLIsw+fzQdd1dO7cGTNmzEAoFMKmTZvQokULrFy5EqFQCFdeeSUkSUIwGIQsyygpKYGqqpAkCW63Gy6XC5qm1dSjFQh+FWdtN0DTNB56+/zzz9G5c2fMnz+fO+B+DafTifLycvh8PmRnZyMcDmPHjh3o1KkTAoEA/vnPf+LCCy+EpmnweDzcibZ+/XpcdNFFcLvd+J//+R+MGTMGgUAApaWlOPfcc/Hqq6/i+++/x0MPPYTi4mIeZisqKkI4HMbu3btx/vnn85Cd1+vFuHHj0KNHD9xwww0oKipCw4YN+bQiEAjA5XIhmUzysJ3Q9ILaptaF3u12I5FIcC3co0cPOBwO6Lp+3DkwYwzvvPMOdu7ciQYNGiCRSODll1/GqlWroGkaZs2ahb59+8Lr9XJT2zRNTJs2DRs2bODaHwB8Ph/uuusu/PGPf4RpmsjNzcWaNWsQj8fRrFkz7NixAy6XC2VlZZg7dy42bdoEXdeh6zquvvpqBAIBqKqKF154Af3790eTJk34QEaefmozxewFgtqkTnjvDcPAgw8+iGuvvRYFBQVgjMHlcvHQGQDEYjEsXboUBQUFyMjIQCgUgizLOOecc1C/fn3k5uaiTZs2cLlcyM3NBWMMXbt2BXB4CiHLMho3boxWrVrB5/MhIyMDrVq1Qr169RAIBNCpUye0a9cOpaWlcLvd+K//+i94vV64XC6MGjUKLVu2RHZ2Ns477zzu9e/SpQu++OILhEIhXHTRRbjgggsAHHYw7tq1CyUlJejduze3DEzTFNpeUOtItV1EY968eejbty8mTZqEjz/+GG63G8lkEk6nEx6Ph8fWJUnCl19+iUceeQTPP/98ndGYlG5LoUVVVVFaWooHHngAU6dORfPmzXkMn4Td6ax1A0uQxtR67ztw4ACuvvpqLF26FMDhGLbf7+cmPiXESJKECy+8EFu3boXb7a7lVh8mHo/D7/fzRB5d1+Hz+VBaWgrDMNC8eXM4HA5EIhGEQiEAEFl5glqn1jU9AO7RZowhGo1CkiT4/X6ekSfLMhRFgcfjwZgxYzBt2jR069atNpvMoRV2TqeTL7rp1q0bNm3aBMMwkJmZiUQiAY/HAwApXxsgEJwstT65tCwLiUQCsizDMAxkZ2dzTzclttBCFwCYP38+Pvnkk1pu9WHISSjLMo/POxwOFBQUwOPxIDMzE4wx+P1+mKYpBF5QJ6h1TU/OOlmWkUgk4Ha7oWkaXC4XXzlHgi9JEmKxGEKhUJ0w8UnDk7DTwER+CVmW4fF4EIvFEAwGwRjjyToCQW1R65pelmXouo6Kigrcd999VZbTUiYdY4x7wLOzs7nZX9u43W5EIhHeRqfTybU5Lfm1LIsPUOSUFAhqk1p35DHG4PF4EA6H8e2338LtdvMlsseGtsjrXZdCXhQ6pDbZl9DafRL2fwWC2qTWhR4AN3ntgn6mmMAkyPb2niltF6QndUdlCgSCGkEIvUCQZgihFwjSDCH0AkGaIYReIEgzhNALBGmGEHqBIM0QQi8QpBlC6AWCNEMIvUCQZgihFwjSDCH0AkGaIYReIEgzhNALBGmGEHqBIM0QQi8QpBlC6AWCNEMIvUCQZgihFwjSDCH0AkGaIYReIEgzhNALBGmGEHqBIM0QQi8QpBknvdnFsVvf0cYOdWDzW4FA8B9w0kJPe7HR/vG00aRpmnyHGtqo0bIs/q/9+y6XC5ZlwbIsOJ1OsSOMQFCDnLR5TxtL0g6tuq5D13U4nU6oqgqHw8F3cJUkCYZhwLIsSJIE0zSRTCb572iAEAgENcdJCz0JLO3H7nQ64fV6oaoqfD4fdF2Hpmn8eNrNlf4fCoUgSRI/h9DyAkHNctJCT5rZ7XbDsiwkEgmoqsp3bmWMcS0uSRKSySQUReF/Y4xB13UYhsGnBAKBoOY46Tk9ae1wOIxQKATgsPaXZRmMMT7HNwwDbrcboVCIz/k9Hg80TYPH4+HfI7+AQCCoGU7Jey9JEtxuNz799FO43W6cddZZyMzMhNvtRjKZhN/vh2ma+Oqrr2AYBrKzs9G6dWtEo1H4/X58/fXXkCQJ9erVQ35+fnXcl0AgOA4nFHpd17nZDhydz8uyjDfeeAOrVq2C1+tF69atceONN6J+/frctF+7di3ef/99FBUVITc3F1dddRU6deoESZIwYsQIXHrppRgwYACuvfZamKbJrQRN0+B2u3mUgCIC5AMAwH82DIN7/+3H0ffId0BTEppy1CZ0X4wxyLLM26PrOneCHjhwAOvWrePHZWRk4A9/+AP3lciyDODwPdJ5agqaotEzpf5AjlrgsDVI1h5N6+j9UJ+y+3ro3VI/s4eB6f4URYHH46nSB+zRI7oGOY+pTfT7Y89P/iTqH/TsFUWB2+3m16C+SW2l9tK1zkROKPT0QsvKyrBy5UqMGDECTqcTmqbh4Ycfxr/+9S/IsowJEyZg9+7dyM7ORigUgmmaeOmll3Ddddfh0ksvxerVq/HGG2+ge/fuWLJkCUKhEJ5++mlomgbDMKqE/Mg5aA8BmqYJXdf5S3K73YjH49B1HW63Gz6fr0rHJ+Ggl2maJhwOB59W1CbUCanz0+BF06EZM2YAOOwzofs1TRObNm1C165dMXDgQD64kXDVFDQw2cO21D6Px8MFxC7s5Lvx+XyIRCLwer1VBg16JjTYA1UHEsMwEA6H4XQ6+f2apsmfXTweh8/n44JObbILNPUNaovX6+XP3OPxVBnIDMPgyofukdqRSCTgdDrhdrtrdKBNNScUerqxyspKrFixAqNHj4YkSXA6ndyJFwwG+bGSJPERORQK8WMUReEv6ZxzzsHdd9+NuXPn4p577uEvhUZZeglOp5O/UIfDwUOCTqcTsViMdwK6tmmaUBQFXq+Xdw4aKI7VqrUJtSEajfJByOFwIJFI4J577sHvfvc75Obmolu3bvB4PJBlGclkEh999BF27twJxhguv/xyyLKMQ4cOoV69ejXWdho87QJJzz4WiyEQCEBVVRiGAa/Xi5KSEjRq1AiyLCMajfJQr13Ai4qK0KBBA27dkZDR+3M6nfw52C01u2VRWlqKzMxM3l8VReHv3O/38+MTiQRcLheSySRkWeZtdzgcSCaTcDgc8Hq9vI8zxhCNRuF0OhEIBLiFQgP2mcoJvfeyLOPGG2/EwIEDsWHDBvTs2RMrV66Ey+WCaZrIyMjggmcfaRVFQTKZ5FrY6/UikUjANE307t0bl19+OZo3b46ZM2ciFotxU4k6kqIosCwLXq8XyWQSuq7zCEA4HEYgEOAa0uv1QtM0bp6pqso1hWmasCwLLpcL0WiU5xbUBbKzs8EYQzweh6ZpmD9/Pnr06IGCggL06NEDwWCwSrJT//79MXToUHz22WfYvHkzNE3jVlVNQdaHoigwTROmaSKRSECWZfh8Pn4v9C5zcnKgKAp/Ty6XCx6PB36/n+dy5OTkcE0vyzLi8TgAcKGk79MgB4Cb6dS/cnJy4HK5+GDh9XoRCATg9/ur9Cu32839TvYEMgDwer1wu91VpiAOhwPBYJAPHNSXaMA6Uzmh0JeXl+Pxxx/HypUrcfHFF2PDhg248sorEYvF+KhHIyGZ/fRiTdPkAqzrOvx+P6LRKNfWzZo1g6qqyMzMhK7r/EX89NNP2Lt3L7Zs2YLt27ejsLCQ/27z5s3Yv38/vv/+exQWFmLOnDm45JJLcMEFF6BDhw7o2rUrHn30UezYsYM7DclKIIuhtqHBiIRH13U8/PDDOO+88zBs2DBEIhHe0XVdh2mayMzMhN/vR5s2bTBnzhwsWLAAP/zwA8+VqEnofUuSxAUZAI/KhEIh+Hw+hMNh9O/fH2eddRZeeeUV3H333cjNzUVBQQEfMOxtJ2shIyODa2VZlpFIJPDnP/8Zl1xyCUaPHo1du3ahrKwMt9xyCzp16oT+/fujsLAQiqLgwIEDGDFiBLp164bbbrsNO3fuRDweRyKRAHA08pSZmQmXy4XKykoA4NMRGjRoANm/fz/Gjh2L3bt3AwACgUCVuf2ZygnvICMjgwtyz549udYJhUJ8NKT/A+CmuaZpfO5N823DMJCVlQWn04mKigp89913aNWqFR8EvF4vduzYgQceeIBrbjLZfT4fkskksrKy8O6770KWZVx22WUYN24c7rvvPp4c5HA4sHTpUsyYMQODBw9Gfn4+Lr744ioOv9rGsiye12BZFl588UU0bdoUo0ePhmmaCIVCfHByuVy88yuKwgXtpZdewqRJk1BQUIB+/frVWNsNw0AwGEQikYDX6+VzebLKTNPkllYwGMT8+fPxyCOP4Oqrr8ZXX30Fxhhmz57NnWoulwulpaVYv359lecyaNAgPk//+OOPcc011+DRRx9FYWEhpk6digsvvBAXX3wxFi1ahB07dmDKlClYsWIFJk+ejHvuuQedO3fG+++/j6effhoPPvggAODQoUMIBAK8D2uahuzsbEQiEXg8Hm7em6bJLck5c+Zg8uTJaN68ObcwdV3n040zld/03ns8HuTl5WHChAkAjjpdRo8ejZkzZ0KSJLRs2RKNGjVCRUUF3nvvPYwcORJXXHEFPvzwQ3zyySeIxWK47LLLsGLFCmzfvh2maeKss87CNddcU8UL3K5dOzz33HPcJKO0XZoeLFu2DC1atEDTpk0xYcIEbk2Ypgmn0wmHw4GRI0fimmuuwYIFC7Bjxw4kEgn07duXO3VqW/DtyU1z585Fs2bNMHr0aGiaxk1Oaic5rGRZRiAQ4NMVh8OBuXPnYuHChQCAAQMG1EjbZVlGLBbDCy+8gMmTJ/O5OQ3q9lyNZDIJj8fD5+QLFizA3/72N35v5Bfy+XzYvn07/30ymUTv3r3h8/lgWRaGDx/OFchrr72G0aNHo7CwkDveFEUBgCrrOwBUmTIyxpCZmYnt27fjzTffxODBg7Fx40ZIkoQhQ4bgmWeeQb9+/dC7d28kEokqUQOySLxeL7755husXr0akiThjjvu4P6sM40TCr3P5wMAPheiF8MYw9SpU7Fy5UpIkoSLLroIzZo1QywWQ35+PjweDwoKChAKhRCJRJCTk4NevXrhyy+/5A9w6NCh/xbmoTx+l8vFOxJZEq+//joURcHNN9+M+vXr845Di3eAw3M9n88HVVVx++23Y//+/Vi2bBkYYxgyZAgXeIoYuFwuRCIRZGRkVOczrgJpeMuy8Prrr+Ozzz7jv6cPZTUyxvg8mjzjsixD0zT4/X60bdsWn3zyCfr27cu/l0wmEQgEqqXt5DmfPXs2Pv30U4wePRrDhg3jgy45xcgqoTnzG2+8gUsuuQQNGjQAcDSb0zAMBAIB3HHHHfB6vbAsC8lkkmt5stBkWca9996LN954A9u2bcNDDz3EpxW6rvMBgq5NjmA6H003MzMz8csvv+BPf/oTxowZg7///e/YtWsXkskkvvnmG1xyySW8bR999BHy8/PRsmVLuN1uuFwufPPNNygqKsLvfve7OjFVPFVOKPR0Y+RlJqFxuVxwuVy4+uqrqxwfDAbRq1cv/vPvf//7Kn/v3r07unfv/m/X0DQNiqLA7/fD7XZzXwDNyd966y1EIhFcffXVyMrKgqIoVTq23dQyTROapiEQCKBZs2YYN24c5s2bB6fTif79+/MBhbQmOWlqCsMw4Pf7MWbMGLzwwgtwu90Ih8OQZZlrDkmS+ABA0EBAUQ2/349LL70UW7duxfLly3H55Zdz/wVFMVI936eQVnFxMZYvX45NmzZh+vTpWL58OXJycpCRkcE944qi4L777sOQIUOwfft23HrrrTxsSoMuTfWuvPJKPs1LJBJ45ZVXkJeXh8zMTO58HT9+PHr27Ik77rgDDRs2RCKRQCKRQCgUQjKZ5O0jJzMpAnLcORwONG7cGG3atEGTJk1www03YNGiRbj11lvx7rvvcsG2LAvl5eXYuXMn/H4/mjZtikgkAr/fj6FDh2LHjh1o27YtV4hnIrXulbB7RGllnsPhgN/vh6ZpePvtt7F161b85S9/4YKgqupxz+dwOLh3lc43Y8YM3HHHHcjOzkZ+fj4yMjIQCAR4Z6BPTUBe68LCQrRu3RrxeBxerxcej+c3px5kdmZkZMA0TdSvXx9ZWVk4dOgQd6RaloWHH34Ys2fPTnkCSSAQQDQa5QN1YWEhgsEg2rdvjw4dOuD1119H06ZNeSx87dq18Hq9eOqpp7hWTyaTCAaD3HIBgJUrVwIAH8zsZrPb7YamaahXrx4SiQR++eUXNGnSpMo7I+uTpkfUl0gBkNKKxWLQNA0dO3bE3r17kZ+fj8aNG3NfSjweB2MMgUAAiqKgQYMGUFWVD2amaWLevHkYOHAgXnrpJTRs2DBlz7YmqRNCb0/kAA5bErquIxwOY/HixVi1ahWPsbpcrhOa4+RMIo3q8XgQiUQwb948dOnSBd999x1P3vD5fJAkqUrHqG5M08TmzZtxzjnnQJZlHg8m7fxrQkrTKpfLxTWix+OBruto3Lgx9uzZg4qKCuTk5GDjxo1Yvnx5FVM3VdCgQtqVYu66rmPHjh148803cd1113Gt6fV60a1bN+7Yo3shTW9ZFrKysiBJEmKxGEKhEDevNU2D1+vFzp07sX37dgCHIwfdunVDfn4+iouLsWbNGuzfvx/du3cHYwznnXcetm/fjqKiIpSUlKBLly7cB+V0OvHpp5+ioqICl19+Oa644gq8/PLLWL9+PdatW4eHH36YP9ePPvoIe/bswW233cZzKL7++mvMmzcPEydORKtWrepEotepUutCT9lP9uwoms+98sorGDVqFI/h/icLc8ijTCEvAMjJyYGmaRg7dixefPFFPi2hZKCajLs6HA48+uijmDRpEr8uCebxBJQEhKYmhNPpxMiRI3HzzTdj27Zt6NWrFy644AI89thjWLZsWcotGPItzJ8/n7dFVVVcf/31aN++PSZOnMjDXaZpYsaMGRg5ciRcLhcf0O0JSbIsIxwOIzMzEx6Ph+dZUCjQsizs27cPn332GQzDQG5uLqZOnQpJkvDmm29i/fr1aNSoEe666y4YhoEpU6bgmWeewcaNG3HuuedixIgRVfw4zZo1Q8+ePaHrOoYOHQqn04kWLVqgXbt2KCkpQYMGDaBpGvLy8tCjRw8exgsEAmjSpAnatWuHDRs2YNq0acjOzk7Zc61pJFYHqljE43FEIhFMnDgRL730Enw+HxRFwaBBg7Bu3Toet6UEihOZrJQWqqoqn99RSM8wDPTt2xefffZZldx9VVWrzfl1LJqm4cYbb0Q0GsXSpUt5SFSW5eMOPiT0ZBWRM5AcZv/93/+NUaNGoXXr1jwGDSDlQk+1ErKyshAKhdCzZ08MHjwYV111FXw+H6LRKILBINeufr8fkUgEbrebO+QotGpZFp8uBINBPhWjAYMSeuxrKeid0jOhmDlZapSURYlhdE7qB8DR9SNU+8GejEOpt+QEpKSurKws/l1VVeHxeM5oTV8nXJDUMellJZNJ3HvvvXxeSrF6u8f2RFAyDuXmk3PJ7/dj2rRpmDlzJhcIsgxqitdffx0XXnghfvzxRzDG4PP5eLLKb0HToFgsBsuyeEhs6tSpWLRoEZ/P0sB3bBjrdKFkoE6dOmH58uWYN28exo0bh1AoBMMwkJGRwePvlIBEWpumKDRw01QmIyODp7YCR4WZpnjkPwCOJteQQFOaNQkpfR84PEjQe6W2UPiN/AT2dgHg2aP2yAHdG92/x+M545eC17p5DxwdfQFwz29hYSE6dOgAp9NZxat97IqnY6EX6HA4EAgEuCccOOzIadOmDdasWYNwOMwdYqlOtGCMQVVV3sn8fj/C4TDWrVuHO+64A/fffz/WrVuH4cOH49lnn+V54/aVYMdi/z1ZJaQZ8/PzsW/fviodG0DK74s03Pr16//Ne23/WZIkrh2P5+W2W2vkuLVjv1/6m/1+7Mcf2x/omrQEnJBlmQ8E9B3yE9HxjLEq/Y1C1cDhVN1j234mUuuanrRdIpHgWnn27NmYMmUKcnNzqyRZAKjy/1/Dfvyx3wkGg2jVqhW6d++OxYsX8wUdqQ5tkaYlZ5ZhGFi7di0+/vhj3HzzzWjatCnq16+PmTNnYvr06fjll19O6p6OvTfTNNGlSxds2bIFyWQSmqZxP8jxvns6H3tO+4na9VvH/Nb9nc75T+a44x1/vPad6dQJodd1HcFgEMlkEj/88ANCoRBP5EglqqrC7/ejdevWsCwLP//8878t80wFFI+m8y5btgw//vgj+vXrh1gshksuuQSWZaFDhw7o378/nnrqqVO+Fs33H3zwQfz1r3/lK8IoLVYgOJY6IfQUo3Y6nfjmm2/QsGFDtGzZslqu53Q60aNHD8TjcXzzzTfc2VNd/OMf/8CBAwcwbdo0/jtKDnK73ejYsSMCgQC++OKLU2oHOaooTx84mvvw/2FxiCD11HqvsCwLlZWV3PFkr3KTajweDyorK/lyXPsa6VTDGMOrr76KsrIyHrumhRoUngSAVq1aYdy4cafsTNR1nafrmqYJv9/PHW40kAoEdmq9R8iyjJycHOzevRsbNmxAhw4dMGPGDJ6Gm2otTGvQ7777bvzxj39EmzZt0L59+5ReAzh8X8OGDeNrzXVdRywWA2OM31cymUQsFqtSAOJkoXi2vfILDWgCwa+RUnX6axpT1/UqnZKOo/8nk0mesWWPg1bXUthoNAqXy4VQKMRj/6kObQHgTkJyFNIyY4q3G4YBn8+HzMxMvkLwVOfg5HWmwg/HrpUQCOykVNOT8Ngrj9AmGNShybyleSelk9rjuNWxWIQgzUhJO1SpJdXYk4jo3il5xG5ypyLRw1540l41qCbXFAjOHFLeI0iDJxIJrs1UVf1VK4CWZFIaLnXS6hJ4KtBoX35pb/OZCA0omqbhpptuwuLFi4WGF5yQlAp9IpHgFUopk07TNGzZsgVXXHEFCgoKMGTIEF7d1L7QBAAvmvFbCTinCgkDJVxEIhFeTeVMxa7dhw8fjjfffJMnHAnhF/waKZUsclBR/rXL5cKWLVuwcOFCPPHEE3xuO3r0aKxevZqXsqbc7FAohPz8/GrrsCQclK7aqFEjlJSUoHHjxmfs+mhaFBKJRPhGIzR9OtMLOAqqh5QKfSwW4/N0qu02ZswYbNmyBcDh+XxxcTEqKiq4aU9JOQDQvn17jB07ls/7U53jbK+BrygKFi1axJfbnslomgafzwefz6b7Af0AABo+SURBVFclL18g+DVSateSlqGQ0erVqzF48GBe9dUwDOTl5UFV1X8rdAEczplu1qzZ4YZVg8lNZi8lBNGCizMde/YfhQj/P9yXoHpI+cTZPkeeNWsWVq9ezf/GGMPChQsxefJkrnEpM82+cQKtcEp1iiytUqN6blRcgf5NNfZloQcOHMCrr76K5s2bpzxEGIvFeI6/JEl8dRqF8lKFJElVLDCqWnxsgpN992JaSGSvCQCAJw+ler2/JEn/tjUatYGUDYU3Ka/BHjKlNlMVHuDong5UriyZTPKQMi0BBsA3/LAXOAWObttlLxNPy4+p/oAkSfwYKvJC9QLpfHZn9+mQ0p5uL+poTzah8JWmaXjllVfw9ttv805JHfSWW27B1q1bMWrUKL6+/Xhe/1PFXhGXOty+ffswbtw4PsVIJbIsV4lErF27Fueccw6vBJMKqCS5oihQVRU//PADRo4cye8xlc+PhMQ+7aKp2LGbR9AiKmqD1+vl6/9JyFK9+QgpCarQSxV47IlLpExIcCiPgp5XTk4OnnjiCUiSxNf/00BBA4e971JdP0p7JqVFwkmCTNcjGQmHw3yLr0QiwVcNxmIxAEdr7FMxUsuyEIlEqpRIP1VSKvSRSASZmZlQVZXvSENbU8XjcUyfPh133303X9JKDrVoNIq77roLU6ZMwaxZs3jBw1SbqFQplqrGulwujB07FnfeeWfKC2TSlIW0yk8//YSPP/4Y3bt3x2233ZbS65DGqKiowLRp0/DQQw9VKS+WymsBh2vIZ2dnY/78+bjwwgvRvXt3bmmQgNm3HAPA20jTPPuai1S2jwSC7v/XBHbWrFkoKCjA+eefz9fl67rOy3XZK/uSFq+oqEBWVhZfumxfl+/1erFv3z40atSI14SwWzXhcBh+v587WiORCLKyspBIJKCqKi8/FgwGuUM5Ho9j+PDhWLVqFX+GwWAwNculWQrRdZ2Vl5czTdOYruvMsix26aWXsvPOO491796drVy5kpmmyUpKSphpmiwej7OysjKmqiorLCxkl112GVMUhem6zkpKSvg5UvVJJBLMMAyWSCSYZVksFouxtm3bss6dO6f0OpZlMdM0WSwWY+FwmOm6zrZs2cI8Hg+78847q+U6qqoyXdfZhx9+yCZPnswMw0j5PUWjUaZpGtM0jT355JNszpw5LBwOM03T2FtvvcW6devGOnfuzF544QVWUVHBVFVlkUiEqarKDMNgiqIwr9fLzj//fLZo0aKUt4+uYxgG03Wd6brOTNNkyWSSVVRUsHg8zubNm8cWLlzIdF1n4XCYFRUVsa1btzLDMJimacw0TaaqKksmkywajbJYLMZ/T+dTVZUlEgkWj8eZpmmssrKSaZrGGGMskUiwgwcPMl3XWTKZZGVlZcwwDHbgwAFWWFjITNPkMhCJRJimaVXepaqqLBaLMV3XWUFBAfv+++9ZZWUlC4fD/P5Ol5RqekmSuBanjLeXX34ZeXl5fBRWVRX169fnBRUzMjJ4bN86UgLKsiy+vRFLobYnM4vmVpQWm5mZmXKrgh0xM5nNL2HfpjqVkGlKu8uQpmE2MzYVBAIBnkhF5i1lVM6YMQNff/01LMvCtddei+7du6NZs2Z8txhJkrB8+XJ07NgRGzdurLK4KlVQODaRSPC2siOhY5fLhZKSEiQSCZx//vn8OX3//ffYtm0bWrRoAUVReL+j6j1UdYf6KJn8qqqiYcOGVWrsU1o31QSkdG9VVbF8+XLEYjHccccdcDgcqFevHmKxGC/jRvvo0fTINE08/fTTuOSSS7Bp0yaeLp6Koi8pdZHTw6H5TGVlZZWXzo6YurQE1O/38zkLVbgNBAK8Sq29PHUqPiSAlAfAGMOkSZN4UcZUfYCj2yLbd6Wxb7+dqg91UCpuAYCb0ABSfi3g6NJdeo72NGPGDm/KSUVEqB2MMZSXl2PYsGF49dVXq6QJp/K5L168GM888wzC4TD+9a9/Yfbs2di3bx8SiQS2bduG4uJiXHTRRXA6nSgtLcV7772HvLw8fPjhh3j00UdRWVmJn376Cffffz82bdqESCTC+/XXX3+N+++/H4cOHUJmZiaeeuopmKaJtWvXYsaMGaioqAAAfPnll5g3bx5mzZqFgwcPYu7cuXj33Xexbt06zJgxA6Wlpbj33nvx7rvvwuPxQNM0LFiwALNmzcI777zDN+dwOp0oKCjAsmXL+M47qZiupVToySkHgHvEg8EgFzgapaiTkrOEfqaOVV1rwanyLgmFaZq46aabcPDgwZRex15lhRbdVNde8pYt197uTbc7j1IFWQ7kfSZnHK2ZUFUVkiRxJyy9XxKaSZMm4cYbb0RJSQnefffdlLYNOPzcW7RogezsbEyYMAFr1qxBu3bt4Pf7+SYh1Bdp9yTTNPHRRx+hadOmeO2111BWVoaHH34YRUVF2LRpE1dAjDE0atQImzdvxt69ezFt2jQYhoGrr74amzdvxsqVK2EYBnbu3InXXnsN7dq1w5o1a7gvwzAMjB8/Hu+99x7279+PpUuXokWLFtB1HYsWLUJubi4sy8Lbb7/NlaTL5ULfvn2xevXq016UZSelvYJGf6fTyTctcDqd3DlCJgzFyMkcswu4fTCojqw8u4OLTCmC8gnKy8t5jfdjj/lPsA9cZHKTNqqOhCPgaAVXeqb2aUUqiUaj3Lllb4M9FGWv4U8DAzsSNcnIyEBubi5+/vnnlK+xcDgc6N+/Pzp37ozS0lLcfPPNGDFiBDIzM7lH3+fzcQeiqqrYuXMnpk6dik6dOiE3Nxfjx4/H7bffjg4dOnBnY2VlJSTpcC3CNm3a4KabbsLYsWPRsmVLZGZmYuLEiWjSpAkSiQTuvPNO3HrrrRg6dChXeH369EGTJk0wYsQI1K9fH2PHjsUHH3yArl274pFHHkFeXh4uv/xyDBo0CMDRiAIpQSp9BoBbE6f1nE77DPaTHWmkPSxDvzvWRPytOmbVRTAY5FtAkxlFGy7SYJOTk3Nao6phGIhGo3w3V0mS+C40qe7oNCe0t7c6YuAA+Jz34MGD8Hg8PIZMAk3XI2vDHnsm857aR9o3lUSjUb63HW2KQteneTNZoIZhoKysDJFIBHl5eXxl6MqVK9GqVSue+8AYQ3Z2NhwOBw8BLlmyBF27dkVpaSkaNmzIl4VbloW9e/cimUzir3/9K6ZOnYpmzZrxd0M76bzzzjto0KABZFlGZWUlVFXFgQMHMHfuXDz22GM4dOgQ39KNFCc9z3r16p32c6r1Iho1iSRJ/MUDR03j7t274/PPP0fbtm2RlZXFa6eTk+pkU1qp3DY5XhRFwc6dOzFq1KiUF+wgZ1MikYDP50Nubi5CoRD27t2Lli1bpnQAtftmfvnlFzRv3pzH3zt27Ii33noLsiyjWbNm/Li9e/dCURSUl5fj4MGDCIfDKCoqwl133fVv+RynSygUAgCsW7cObdu2xc8//4yzzz6b75lH74M21Ni2bRu6d+8Ot9uNr776Cp07d4YkSTh48CAYY2jVqhUPQ2uahv379yMYDCI7OxtlZWV47rnn8O6772L79u1o1aoVXC4XiouL8Ze//AXjxo2Dz+dDOBzGli1bkJeXh5UrV6JevXo8VZ2mQC+//DLWrl2LRYsW4aeffkK7du24dUhKwq6o6pQjr65DpjrFb6lgx4ABA/DEE08gJyeHj6o0wp6KOU7WCtVP9/l8mDVrFpYsWYIxY8ak/J6sI0U5TNNEy5Yt0aRJE7z33nspN+8pe2zXrl3Ytm0bBg8ezB1yM2fOxNdff43Nmzdj8uTJyMnJgWVZOHToEIqKirBnzx589dVXqKiowK233nrKU6cTwRjDM888g/LycgwZMgRTpkzB1q1befo3O5IkRM/rnnvuwdlnnw1d17FkyRIUFBQgMzMTO3fuxJo1a5Cdnc2dzZIkYd26dWjUqBHat2/Pp4iMMbz44ovQdR2BQACTJk1Cly5dsG3bNqxatQolJSV44IEHkJOTg7///e8YNGgQ3z/P5XKhV69e+P3vf4+uXbtiwYIF2L17d5UMR9LwtFVYKqw3efr06dNP+ywpIB6PY9myZRg3bhyA6qn6Yjft7Hva16tXD6WlpTh48CBat27NlwUfm475n0KdRJIO79E2d+5cjB8/Hueee27Kpy9kXlMHpLTQzz//nJfaTuW1otEoFi9ejIKCAjRq1Ig7R7OystCzZ09069aNVwRyOBxo0KABGjdujLPPPhsDBgxAp06dAIA7N1P9nktKSjB48GDk5OQgEAigRYsWqF+/Pq9+vGvXLgwcOBAOx+HEm/z8fJx11lmoV68ezj77bAQCARiGgfr166NFixZ8GkJO6caNG6NRo0aQZRn16tXj53e73ejatSvOPvtsxONxZGZmYuTIkahfvz4aNWqEtm3bYsiQIWjVqhW8Xi/vU/n5+QAOa/L27dtj8ODBXJM7HA4UFhbi22+/Rf/+/fnc/rSto9OO9J8mlJhQVFTE+vTpw3+uDiiBgpIvLMtiuq6zSCTCnnzySTZ79myeGEEJGKZpnvR1LMtihmEw0zSZoijswgsvZCUlJUxRFKaqakrvSVVVpigKM02TlZaW8qSniRMnsnXr1qX0WpFIhFVUVLCLL76Y6brODh06xJNwKHlFVVWelEOJPJQoE4vF+DNRFCXl75muGYlEeDJQPB5n8XicGYbBVq1axaZMmcJKS0tZMplkiUSChcNh/qHnSH+Lx+M86Wnfvn1M0zTeL+i5UwIZJQApisIqKipYNBpluq4zwzBYYWFhleOLiopYcXEx7yeUXEXPxjAMFo/HWUVFBRszZgz75ptv+POjPnw6pJV5T440mlNZR6rGBoNB5OTk8LJdsVgMTqfzuLvI/ieQCRkOhxEKhXjOdKq99zSnN02T7+fu8XjQuHFjhMNhviW0PemD/YbZz45YD/aPdWTvucLCQuTm5vItnEmjUz4CmftUmNPu0KPVgDRfTbV5HwwGoSgKzw0hRypFG/r27YsmTZpgxYoVfONSv98Pt9vNP5RX4PV6uUOQtDppfNogldZWkFWYkZEBWZYRCoX4MmcAaNiwYZVcgry8POTl5fEUYHs0hJ6Vz+dDRUUFDh06hHPPPZdfr86l4Z4KNanpjwelP951111sxYoVPE2XUiZP5XyKorBkMsnGjh3LNm/ezLXQqZzvVOnVqxcrLi5m4XCYxeNxxhhjxcXFJ0zlJOvHMAymqirTNI0lk0kWiUSYoiisbdu2/HeJRIKnptZ1EokE0zSNvfnmm2zOnDmspKSEP5O6AD13skIVRWEXXHABSyaTKb9WWmn648GOJA6R842KgJwqFLIkDcyOlL22Z8rVBLSTLIX0aKnmiaBnQdtj0TNhRzQ+aVPSOvYtwesybrcbiqLg8ssvx1lnnYVDhw7VqV2A2BHfEYW1VVXFDTfcAFVVU34tIfQ4Gle+4oorsGHDBhw8eJCnl55qp6BMr4suughNmjTheeA1Wbdu2rRpWLhwIZ+mGIbxH+0lYI86SJIEn88Hp9OJxx57DDfccEOVfIxUeZSrG0oeUlUVw4cPR5s2bXjoti5AgyolVwUCAVx33XXVsn9B3X9bNQBp5i5dumDnzp2IRCJQVfWU51AUC96yZQvq16+P3NzcKiGemqJ3795Yt25dlW2ff0tzSNLhLZ5pnqmqKvbu3QvDMPDRRx+hX79+8Pv9kGW5SgZmXYfCjbTI6uDBg3VqsCIfB1lO7IjvQ1GU1F8r5Wc8A6GFIpqm4dlnn8Vtt93GTfFT0QaMMaxatQo+nw9Dhw5FOBwGcDijrab3Nl++fDnGjh0LVVXhcrl4CfDjQYMSOTpdLhfq1auHefPm4ZZbbuFZZOzIwhpN06pt74BUQtZNMpmELMvIy8sDUD1l2U4FTdP4VJCUjWmaQtNXF4wxnhqamZmJV199FQMHDuSe2pNl165dWLp0KW677TbuzaV5dao91idClmU0adIEEyZMwIwZM7hH+7fm9TTglZaWwuFw4KWXXkIoFEK/fv3QtGlThEKhKsU3U12ApDqIRqN8qzT7isea9LGcCErAsUc2qI2p5jeFnuai5Myx/45ykalEEHVo+pvdlKUOR3MXqj5ix378b4WWjj0ffYdMI/t57FtrUTvp/DTPpnAemav9+/fH6tWrefqj/Z7t56dNPcgiMAwD7733HgYNGgRZlvkiIwC14jjSNA35+fnIyMjAjh07uAahZ2F3NtJ9Uadr2LAh9u7di4qKCnTs2LHKGnMKd1bX9mOpJjMzk9d6YEdqHZAlUxegZ0hzekmSkJWVVS3X+o+FngQlFoshkUhw7zY5vOzCTMtXVVWFaZp8fTVjhzeYoNGV9q6zCxE5kU4EeZftxx17Hk3T+BpkALyT2oWOOi/dG81NJUnC7bffjm+//RYffPABbxcNVDTI0T3TwKfrOubMmYMGDRpg4sSJVRYUeb1evtKwpqBFIy1btsSoUaPw5ptvYtu2bfzegaoDLb0/ALxYxIIFC3D++eejb9++/F4oxu3z+aosoqrLkOOR0lkB1Kky4eQQta8+rS5OeGbqNCQY9NACgQCGDx+Ovn374plnnqniHKIBYsmSJRg8eDBuvPFGvjyQMYa//e1vGDJkCO6++26uBTVN4/NMClucyAymjkeVSe3VSXVd54UPyHlDHZyWecbjcSSTySrmEw0KtD68QYMGGDNmDNavX49+/frh4MGDVdapOxwOvhQXAJYuXYr+/fvjnHPOwVVXXXV6byVF0CpCSZLQoUMHjBkzBvPmzcOIESN4bQO78NNzZIzhzjvvxIgRIzBy5EgMGDCgiqUnOMM5URDfNE0WjUZ5qmA0GmWKorA+ffqwH3/8ke3fv5/Nnj2b/eMf/+C1yRKJBHv88cfZ4sWL2YEDB9jmzZvZqFGjmGEYrKioiPXo0YNt3LiRFRcX87RU0zTZgQMH2IABA3iKI6Uo/tonmUyyQ4cO8cSQXzuGUj+pVhylWNprndnTLmOxGIvH47yOHh0TDofZgQMH2LBhw9iwYcPYnj172IEDB1hpaSkrLS1ln3/+OevSpQt74IEH2L59+9jBgweZoignnzFRTVCSTSKRYJWVlfyddOvWjd15553sl19+YcXFxaysrIyVlpayZ599lrVt25atWLGCFRUVMU3TWDQaZRUVFTWeNCWoHk4YayFnTWlpKerVq8dNjsrKSr7YghIJyDym6rYej4enhYbDYSiKgueee447T7Kzs/n5SVvbK+TS/PrXTEcygUjL0jJFu/eTUiqpnDazTT/i8TiCwSA/n6IovO3FxcXIzc3l56KUztdeew179uzB+PHjeaKHaZpo3rw5/vnPf/JnE4vF6sx2UowxVFRUQJIkZGZm8tWDoVAIn3zyCd5//31cd911fGrEGMPgwYPx7bffVkkWIa8/q+E8A0H1cEKhX7NmDX755RceL7zooovQpUsXXlzAXnxRUZQq+69nZGTwtevUqaZNm4Y///nPuPPOOxGJRNC3b1/uTPH7/SgvL8dLL730m0UTGWNo2bIlevXqxc9N69dVVcW6deuwZ88e+Hw+7mOgGDkVzKBqPn379kVeXh5kWYaiKGjQoAH/zrJly/g0IxQKobKyEuPHj0dFRQWvvOP3+/Hyyy+jQ4cO6NatG7Kzs1P7hk4DwzAQDAb5qkGfzwdN03jlmIEDB+LKK6/kmXdk7tNUhzL6gMNOyOqeawpqhhMKvWEYiEQivP4Z7UZLBRIYO1qIn8I2pIUJWvhP80tZljFx4kRMnToVPXv2rNKRGGM8pk2hi+NpFnvBSfvPwGHNTY4+8k6Tz4A2J6BiBOQ4JG0GHJ77x+NxRKNRfn5yCtI211QAIRKJ8OiAffFLXUlYYUeqtdJCDvrQ4hFayEEWmL1uIWUqkuMrlQUvBLXHCXvmoEGDMGTIEK51yXROJBK85hhwdJMBu3a2F4UEUCU2ChwdDOwmfF5eHv70pz9xrXw8gScrg4TWvmuJz+fDFVdcwQcMmjJQm+i79g0N7DucAIe1WuPGjTF16tQqYUoK89idf7STCl2Dfq4L2Nes033bt0k6tq32d0HPIxgMVnGECs58Tij0dqEmqLAk1fi2V12trKxETk4OXC4X15Tmkb3qyGQuKirC1KlTsWTJEi5AdH77lkkn6mD2emx0vL2Ndi17rMa1f5fu79fm4PbwHXA0vGPXdsee59jf1zb2Z0Ia/FjsbT1eu+uK1SJIDSfdO71eLzZs2IBRo0ahV69e8Pv9GD16NBhjuOmmmxCJRDB58mSUlZWhT58+uOuuu7BixQq88cYb6NOnD8aPH4/nn38ejRs3rjOJEQJBOiGxE3nMfgWKc1OCBpnsZC6TE4hKAoXDYQSDQV5Smjzr9lLUkiShpKQE1157LdasWXO4YcJLLBBUCydtt9F2UOS0Ag47zsj8tZc8prk/CTB5z8+k9E2B4P8bJ23e272+tMKKQnM0ZyRtby8OSWWqAPAQEnmLBQJBzXHSmp6cPRQTpyozFLIjzzD9n5xAjB3dH1xRFJ4cY/d8CwSC6uekhZ6EmGLvQNWllcdueQT8u3ebNqsEUr+Dq0AgODFCxQoEaYYQeoEgzRBCLxCkGULoBYI0Qwi9QJBmCKEXCNIMIfQCQZohhF4gSDOE0AsEaYYQeoEgzRBCLxCkGULoBYI0Qwi9QJBmCKEXCNIMIfQCQZohhF4gSDOE0AsEaYYQeoEgzRBCLxCkGSdd9z7V0OUty0JFRQVyc3MPN0xUyRUIqoVaF3qBQFCzCPNeIEgzhNALBGmGEHqBIM0QQi8QpBlC6AWCNEMIvUCQZgihFwjSDCH0AkGaIYReIEgzhNALBGmGEHqBIM0QQi8QpBlC6AWCNEMIvUCQZgihFwjSDCH0AkGaIYReIEgzhNALBGmGEHqBIM0QQi8QpBlC6AWCNEMIvUCQZgihFwjSDCH0AkGaIYReIEgzhNALBGmGEHqBIM0QQi8QpBn/B7y7sO/80g5fAAAAAElFTkSuQmCC)
A plane progressive wave is shown in the adjoining phase diagram. The wave equation of this wave, if its position is shown at t=0, is
![](data:image/png;base64,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)
physics-General
physics-
A rod PQ of length ‘L’ is hung from two identical wires A and B. A block of mass ‘m’ is hung at point R of the rod as shown in figure. The value of ‘x’ so that the fundamental mode in wire A is in resonance with first overtone of B is
![](data:image/png;base64,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)
A rod PQ of length ‘L’ is hung from two identical wires A and B. A block of mass ‘m’ is hung at point R of the rod as shown in figure. The value of ‘x’ so that the fundamental mode in wire A is in resonance with first overtone of B is
![](data:image/png;base64,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)
physics-General
physics-
The length of the wire shown in figure between the pulley is 1.5m and its mass is 12 gm. Find the frequency of vibration with which the wire vibrates in two loops leaving the middle point of the wire between the pulleys at rest
![](data:image/png;base64,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)
The length of the wire shown in figure between the pulley is 1.5m and its mass is 12 gm. Find the frequency of vibration with which the wire vibrates in two loops leaving the middle point of the wire between the pulleys at rest
![](data:image/png;base64,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)
physics-General
physics-
In a sonometer wire, the tension is maintained by suspending a 20kg mass from the free end of the wire. The fundamental frequency of vibration is 300 Hz
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)
If the tension is provided by two masses of 6kg and 14kg suspended from a pulley as show in the figure the fundamental frequency will
In a sonometer wire, the tension is maintained by suspending a 20kg mass from the free end of the wire. The fundamental frequency of vibration is 300 Hz
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)
If the tension is provided by two masses of 6kg and 14kg suspended from a pulley as show in the figure the fundamental frequency will
physics-General
physics-
A train A crosses a station with a speed of 40 m/ s and whistles a short pulse of natural frequency
. Another train B is approaching towards the same station with the same speed along a parallel track. Two tracks are d = 99m apart. When train A whistles, train B is 152m away from the station as shown in fig. If velocity of sound in air
, calculate frequency of the pulse heard by driver of train B
![](data:image/png;base64,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)
A train A crosses a station with a speed of 40 m/ s and whistles a short pulse of natural frequency
. Another train B is approaching towards the same station with the same speed along a parallel track. Two tracks are d = 99m apart. When train A whistles, train B is 152m away from the station as shown in fig. If velocity of sound in air
, calculate frequency of the pulse heard by driver of train B
![](data:image/png;base64,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)
physics-General
physics-
Two tuning forks P and Q are vibrated together. The number of beats produced are represented by the straight line OA in the following graph. After loading Q with wax again these are vibrated together and the beats produced are represented by the line OB. If the frequency of P is 341 Hz, the frequency of Q will be ___
![](data:image/png;base64,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)
Two tuning forks P and Q are vibrated together. The number of beats produced are represented by the straight line OA in the following graph. After loading Q with wax again these are vibrated together and the beats produced are represented by the line OB. If the frequency of P is 341 Hz, the frequency of Q will be ___
![](data:image/png;base64,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)
physics-General
physics-
AB is a cylinder of length 1m fitted with a thin flexible diaphragm C at middle and two other thin flexible diaphragms A and B at the ends as shown. The portions AC and BC contain hydrogen and oxygen gases respectively. The diaphragms A and B are set into vibrations of the same frequency. The minimum frequency of these vibrations for which diaphragm C is a node is (Under the conditions of the experiment the velocity of sound in hydrogen is 1100 m/s and oxygen 300 m/s)
![](data:image/png;base64,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)
AB is a cylinder of length 1m fitted with a thin flexible diaphragm C at middle and two other thin flexible diaphragms A and B at the ends as shown. The portions AC and BC contain hydrogen and oxygen gases respectively. The diaphragms A and B are set into vibrations of the same frequency. The minimum frequency of these vibrations for which diaphragm C is a node is (Under the conditions of the experiment the velocity of sound in hydrogen is 1100 m/s and oxygen 300 m/s)
![](data:image/png;base64,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)
physics-General
physics-
A heavy but uniform rope of length L is suspended from a ceiling A particle is dropped from the ceiling at the same instant the bottom end is given the jerk. where will the particle meet the pulse measured from bottom?
![](data:image/png;base64,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)
A heavy but uniform rope of length L is suspended from a ceiling A particle is dropped from the ceiling at the same instant the bottom end is given the jerk. where will the particle meet the pulse measured from bottom?
![](data:image/png;base64,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)
physics-General
physics-
A heavy but uniform rope of length L is suspended from a ceiling If the rope is given a sudden sideways jerk at the bottom, how long will it take for the pulse to reach the ceiling?
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)
A heavy but uniform rope of length L is suspended from a ceiling If the rope is given a sudden sideways jerk at the bottom, how long will it take for the pulse to reach the ceiling?
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)
physics-General
physics-
A heavy but uniform rope of length L is suspended from a ceiling Find the velocity of transverse wave travelling on the string as a funcition of the distance(x) from the lower end
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)
A heavy but uniform rope of length L is suspended from a ceiling Find the velocity of transverse wave travelling on the string as a funcition of the distance(x) from the lower end
![](data:image/png;base64,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)
physics-General
physics-
A detector is moving in a circular path of radius r in anti-clock wise direction with a constant angular velocity w as shown in the figure. At time t=0, it starts from the location shown at A, assuming source at rest. The time interval between minimum and maximum frequency as received by the detector
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)
A detector is moving in a circular path of radius r in anti-clock wise direction with a constant angular velocity w as shown in the figure. At time t=0, it starts from the location shown at A, assuming source at rest. The time interval between minimum and maximum frequency as received by the detector
![](data:image/png;base64,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)
physics-General
physics-
A detector is moving in a circular path of radius r in anticlock wise direction with a constant angular velocity w as shown in the figure. At time t=0, it starts from the location shown at A, assuming source at rest. The time at which the detector will hear the maximum frequency for the 1st time
![](data:image/png;base64,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)
A detector is moving in a circular path of radius r in anticlock wise direction with a constant angular velocity w as shown in the figure. At time t=0, it starts from the location shown at A, assuming source at rest. The time at which the detector will hear the maximum frequency for the 1st time
![](data:image/png;base64,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)
physics-General
physics-
A detector is moving in a circular path of radius r in anticlock wise direction with a constant angular velocity w as shown in the figure. At time t=0, it starts from the location shown at A, assuming source at rest. The frequency as received by the detector when it rotates by an angle ![fraction numerator pi over denominator 2 end fraction](data:image/png;base64,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)
![](data:image/png;base64,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)
A detector is moving in a circular path of radius r in anticlock wise direction with a constant angular velocity w as shown in the figure. At time t=0, it starts from the location shown at A, assuming source at rest. The frequency as received by the detector when it rotates by an angle ![fraction numerator pi over denominator 2 end fraction](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General