Chemistry-
General
Easy
Question
In the reaction, 2CuCl2 + 2H2O + SO2 → A + H2SO4 + 2HCl ; A is
- Cu2Cl2
- Cu
- CuSO4
- CuS
The correct answer is: Cu2Cl2
Related Questions to study
physics-
The variation of PE of a simple harmonic oscillator is as shown. Then force constant of the system is (PE 'U' is in joules, displacement ' x ' is in mm )
![](data:image/png;base64,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)
The variation of PE of a simple harmonic oscillator is as shown. Then force constant of the system is (PE 'U' is in joules, displacement ' x ' is in mm )
![](data:image/png;base64,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)
physics-General
physics-
A particle at the end of the spring executes S.H.M with a period
, while the corresponding period for another spring is
. If the period of oscillation with two springs in series is ' T ', then (same particle connected in all the cases)
A particle at the end of the spring executes S.H.M with a period
, while the corresponding period for another spring is
. If the period of oscillation with two springs in series is ' T ', then (same particle connected in all the cases)
physics-General
General
The flagpole and ground are ________ to each other.
For such questions, we should know about perpendicular lines and parallel lines.
The flagpole and ground are ________ to each other.
GeneralGeneral
For such questions, we should know about perpendicular lines and parallel lines.
General
Identify the perpendicular lines in the given figure.
![](data:image/png;base64,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)
For such questions, we should know about perpendicular lines and parallel lines. We should start with horizontal lines or verical lines. We should follow the order or there are chances to miss the lines.
Identify the perpendicular lines in the given figure.
![](data:image/png;base64,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)
GeneralGeneral
For such questions, we should know about perpendicular lines and parallel lines. We should start with horizontal lines or verical lines. We should follow the order or there are chances to miss the lines.
physics-
Acceleration displacement graph of a particle executing S.H.M is as shown in given figure. The time period of its oscillation is (in sec)
![](data:image/png;base64,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)
Acceleration displacement graph of a particle executing S.H.M is as shown in given figure. The time period of its oscillation is (in sec)
![](data:image/png;base64,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)
physics-General
physics-
The time period of a particle performing linear SHM is 12 s. What is the time taken by it to cover a distance equal to half its amplitude starting its motion from the mean position ?
The time period of a particle performing linear SHM is 12 s. What is the time taken by it to cover a distance equal to half its amplitude starting its motion from the mean position ?
physics-General
physics-
A small mass particle is given an initial velocity
tangent to the horizontal rim of a smooth hemispherical bowl at radius
from the vertical centreline as shown at point A. As the particle slides past point B, on a vertical distance h below A and a distance r from the vertical centreline, its velocity v makes an angle
with the horizontal tangentto the bowl through B.
![](data:image/png;base64,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)
A small mass particle is given an initial velocity
tangent to the horizontal rim of a smooth hemispherical bowl at radius
from the vertical centreline as shown at point A. As the particle slides past point B, on a vertical distance h below A and a distance r from the vertical centreline, its velocity v makes an angle
with the horizontal tangentto the bowl through B.
![](data:image/png;base64,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)
physics-General
physics-
A rectangular rigid fixed block has a long horizontal edge. A solid homogeneous cylinder of radius R is placed horizontally at rest with its length parallel to the edge such that the axis of the cylinder and the edge of the block are in the same vertical plane as shown in fig. There is sufficient friction present at the edge so that even a small displacement causes the cylinder to roll of the edge without slipping. The angle
through which the cylinder rotates before it leaves contact with the edge is
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)
A rectangular rigid fixed block has a long horizontal edge. A solid homogeneous cylinder of radius R is placed horizontally at rest with its length parallel to the edge such that the axis of the cylinder and the edge of the block are in the same vertical plane as shown in fig. There is sufficient friction present at the edge so that even a small displacement causes the cylinder to roll of the edge without slipping. The angle
through which the cylinder rotates before it leaves contact with the edge is
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)
physics-General
physics-
A uniform circular disc has radius R & mass m. A particle also of mass m is fixed at point A on the edge of the disc as shown in the fig. The disc can rotate freely about a fixed horizontal chord PQ that is at a distance R/4 from the centre C of the disc. The line AC is perpendicular to PQ. Initially the disc is held vertical with the point A at its highest position. It is then allowed to fall so that it starts rotating about PQ. Find the linear speed of the particle as it reaches its lowest position.
![](data:image/png;base64,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)
A uniform circular disc has radius R & mass m. A particle also of mass m is fixed at point A on the edge of the disc as shown in the fig. The disc can rotate freely about a fixed horizontal chord PQ that is at a distance R/4 from the centre C of the disc. The line AC is perpendicular to PQ. Initially the disc is held vertical with the point A at its highest position. It is then allowed to fall so that it starts rotating about PQ. Find the linear speed of the particle as it reaches its lowest position.
![](data:image/png;base64,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)
physics-General
physics-
A uniform disc of mass mass and radius r rotates along an axis passing through its centre of mass and normal to its plane. An unstretchable rope is wound on the disc. Tangential acceleration of a point P on the periphery of the disc when a uniform force
is applied on the rop is
![](data:image/png;base64,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)
A uniform disc of mass mass and radius r rotates along an axis passing through its centre of mass and normal to its plane. An unstretchable rope is wound on the disc. Tangential acceleration of a point P on the periphery of the disc when a uniform force
is applied on the rop is
![](data:image/png;base64,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)
physics-General
physics-
A uniform disc of mass M and radius R is supported vertically by a pivot at its centre as shown. A small dense object of mass M is attached to the rim and raised to the highest point above the centre. The unstable system is then released. The angular speed of the system when the attached object passes directly beneath the pivot is
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WkOb9IkSJyPrR8+XLjisYROtq3a9dOirFly5Z6meMV0CIMB62ANNtzDY3eKlxc15bBF0Pn7WbNmkkx0utHOwFEHS1CB3bv3i3X9zjfoceKXid7eRYvXiyNVnRKWLp0qZGreR5ahAL6VH777bcoUKAA2rZtK9f9NK8OQ/vTgkwHc6450sVOEzkeL0IOo7gTgy03LX+amIP+rnTRo1GLa6qaiPFoEdJ3k71fx44d9RzGifA4gbx588qN2jpA1H/xSBHSYZq7GAoWLCgPXNE4H1pROVfkGisX/zX/4nEipBM1KwN3NWhzumvh5mSOOvLly4dZs2YZuRqPEuHKlSuRP39+uY1IH4riPrhPMleuXPIIOI0HiZBuZjlz5pTzE437ob8tG8RevXp5fLh9jxAhW1wKkJtaNeZh7969KFOmjNxk7MlR2mwtQvp4sqWlBZTHgGnMBx3jGXaDm4mtsvcyprG1CClAer9oa5y54cGlPCuSW6U8MZqbbUVI52suQXAxXmN+uH7IoFRM9LjxJGwpQsZ4yZMnjz740mJwNz+HpjyBOLLwjHbEdiJkrE0aYTZs2GDkaKwEw2cw6jmdKTzFamorEXILUo4cObBs2TIjR2NFGF+VcW24mdoTsI0IaXyhJ8b06dONHI2VYWBiTik84f9pCxHS+Zrh+Rg/U2MfuK5Lx2+7x7GxhQg5f+B2JO2hbz/oYkhfX2dHKXcnlhehn5+f3Dxql3ifmmfhGR61atWS8WseP35s5NoLS4uQ8wbOAxlSQWNfaKhh7Bo2uHbEsiJk/BduR9LzQM+AO/M54rFj6BHLipBnJjAQr53nCppn+eyzz6SzNw9OtROWFOG5c+ekTygPwNR4Dpz3szdcsmSJkWMPLClCHsLCAEJ2axE1L4ahKBkTli5udsFyIly1apXcmsRTbzWeB31KecApTxu2C5YSIX0JGSiIOyQ0ngtDU3JYypCKdsBSIly0aJE8mssT95xpnoX7D3v06GG8sjaWESHnfzwViceTaTSMlFCsWDG5M9/qWEaEnAvyS9cnxWoIpyb16tWzxdzQEiLkqUgffPCBx2xt0UQNLlVwehIUFGTkWBNLiJAbdLkuqP1DNY48fPhQ7sTn4TNWxvQi5FyQUZu/+uorI0ej+ZfJkyfLcyTp6G1VTC9CWkLLlSunz7rTRMilS5fkkNTKx3WbXoQLFy6UMUc8OTis5vnwzPzu3bsbr6yH6UXIL1jvlNA8DzbUdGW7e/eukWMtTC1CNdTYtGmTkaPR/Bee9kQRWnVfqalFOHXqVOknSCuYRvM8OnXqJMOcWBFTi5AWUbu4JmmcC9cMeeT5jRs3jBzrYFoR0lueEdQYS1SjeRGHDx+WAaEY8sRqmFaEPDaL4/xDhw4ZORpN5HCdkBH3eACp1TCtCGfPni2/VL00oYkqnBd27tzZeGUdTCtCrvu0bt3aeKXRvJgpU6bInTZWW6owpQg5tKhbty4mTZpk5Gg0L4bzQXpXnT592sixBqYUIbcrcWmCO6g1mqjCqUuFChWwfv16I8camFKEytKlD/jUvCyMRWs144wpRbht2zaULVsWwcHBRo5GEzV4wOjQoUONV9bAlCJcsGCBHI56yiGRmpiDfsZWc/AwpQh/+uknGchHo3lZfH19pdO/lTClCHv37o127doZrzSaqMNDRblMYSVMKcK2bdti4MCBxiuz8QRXzhzE5vWB2LB5J85cse6ObjuyYsUKadRjXCKrYEoRMsz94MGDjVcmIjQEa8d3QumsKRArViyR4iHb2/Ux4fcTsOfJedZj3bp1chM4T+2yCqYUIcf05rNwPca+WV8jYwKK79kUP0tVzNhjPe99O8IwFxShlU5tNp0IGdipefPmGDFihJFjDp7cP43ePq//R4BPU1xU7zkf1tzXbS+2bt0qF+yttKXJlCLkGXTDhw83cszBo+sb0DhHoggE+DQV/mgodFhi97NlyxYpQis5/ptyOMrzyYcMGWK8MgdP7h1D13KpIxRgrFhxUKXLDDxvALRjxw74+/trBwQnQ5c1DketFALRlCLkjvpBgwYZr8zCI/zp9wVSRyTC9KUxflPkh9SsXbsWWbJkQdy4ceV2m8ePtRnHWfC7pgitFBLFlCLknrCePXsar0zEgyDMHNAUub2SGgKMDa/cFTFw1nZE5ttz5MgR5M2bN0ywzZo1055AToTeVgwGbKUDZE0pQp4/SOOMOXmI49tXY9b0KZg+eyG2H4/8zPzLly/L6ABKgN7e3jJigMZ5jBs3Do0bNzZeWQNTilBtzrQy7O14pLcSYJo0aeTJUhrnQicPq3lbmVKEPHuOXg9WDW3BoVCfPn3CBJggQQL4+fkZVzXOhNEYrHZcmilFuG/fPrlD+uTJk0aOteAhJUmSJAkTIb36Y3SO8uQfXDt3DPsOHMKZ4Igbqif3Q3Dy2CHsP3gCIfdDjVz706BBAzkktRKmFCHFx3CH3FdoNWidS5UqVZgAOT958OCBcTWGePIYd85vRvd6JeBd/GOs/c+qRyiW9Hsf2fJXxJAFB/B3qGdYY0NDQ6VRhseqWwlTivDq1asy0lpAQICRYw0OHDggjS9KgFw0pnHGOdzDjK/fQ+JY8dBk5GYhu395dGElmhZOjthvVkWANQcTr8S5c+dQpkwZ7Nmzx8ixBi4Q4SOc3xOIX/xGwXfoUPgO8cWwYSMwbtpCHAiOuIegB/xnn31mqfPpL1y4IIfQSoC5cuXCwYMHjavO4A6WjvJFm/dzI3PZz/HnVSNbiHP9xB/RsUlpZC3VCEutf6R7lOEOCo6geJyelXCBCB/j5sVDGPFFKcSPkxsD5wdiQ+A8dKpdHNlLNMCMHRF/YdzYyyOyrbCmxmjhjpbQtGnTYuXKlcZVZ3ETC8eMxdzfhsHHOwdaTX7a+j85GwjfwWMw27cV8peqi0XWCjwWLehlxf8Dh6VWwmXD0XUjmiB9mspYbvjV/n3YHwXixkKhT0cjIkcuzq18fHxkD2N2uAlZCTBevHiYOHGiccWZ3MTc4T/hjyMHMbNLeWQq3w3n/3mIXb/9hFEzt+FIQFfkKlLbY0RIL6SmTZuacwvcC3CZCNcOa4KM6SpjcbCx2fLeGlRNHgc56n6Pc09znkEN7zZv3mzkmBMKLn78+GEi5NKEa7iBub5Dsfp0CG7snYLSWXLi64kBGCcq4Ybgx7gyrw2yF/YcEfIYPTbazh+BxDwuFGFTeKUtg+mHr+LmrWtYMbgR0qfLh37zDz1jVFDQpF+/fn2MHj3ayDEfnIOkTJkyTICM9OU6n8W7CBg5EiuPcWgRgtGfFEKCdAXRcfRGMQsHgua0QY6idbE8SL7Z9tCSTkPYqVOnjBzr4DIR/j7yE3gl98ZXA/qjcflcyF7mI8zcclpWmMig98Onn35qvDIXdD9ztITyWC62xq7hCe5c3om+TRph4Oz1uCF0f3HFQBTJ/w7mnnyE0NuXsaxnRcRKngeDV5zBvVDr+FG+KlwbrFOnjuXmg8Slw9E3MryDpWfP4tcOZZEyS1UsOPF8owuHom+//TaCgszVnFNsjIuqBEgxOtcSGp7HuHpsIyYOHwK/BesRxD1UoRewZctB0N587/JxLJ00BL37fo9flv2FkIf2XiekNZ2jJkZasyKunRO+XhlLxOjpye3d+LLk68hcpScOPycUCL/c6tWry314ZoEL71yAVwKkJZRGJI37YMT2kiVLurghjDlcJsKNoz6GV5rKWBry9PWVzWNQME1yVO+zAM+bRf34449o2LChKbam8Bl4WpQSYMKECTFt2jTjqsZdsAdkT2hVXCDCx7h4IBDd3+f8KTW+mrwWZ66x+3uE9SMaIWmclHiv02is3XkmQjFy7lWqVClTHBbKeQeXICjA2LFjY8CAAcYVjbvgHJDeVa5ZFnIOLhHhtdN7EbhiERYuXIg1m/ch+JbhKRN6HVuXzcOv85Zh57HgCDfGcvjHCffIkSONHPewfPny/1hCrRRWz64wsBOHomfOWNc1yGXD0ejw888/o2rVqtIzxR1wV0eOHDnCBEhLKP1bNe6nW7duMlqBGaYrr4olRHjx4kVpJWVP6moYmKl06dJhAqRP6NGjR42rGnfCw0CLFi2K1atXGznWxBIiJAx5Ubt2bZeuAzFiF41CSoDp06fHH3/8YVzVuBuuI9erV89SQZ0iwjIi5Fph8eLFXdbq0ReRQx0lQO6O15ZQ88C1Ws4FlyxZYuRYF8uIkPTt21furHBFyEBaQrkEoUSoLaHmgssStIpa0UMmPJYSIXfccw7AQz+cCX1CU6f+N9AvXedifHe85pWhUYzLVvPnzzdyrI2lREi4bciZc8Pdu3fLQL1KgNwkGhJieBhoTAEDOdGTyl3W8pjGciLk3JCtoDNc2VTZSoB58uTRllCTwUYyf/78CAwMNHKsj+VESGbNmiWHpefPx9wRLAyvyPmmEmCGDBmcPuzVvByMskBrdfv27S29LhgeS4qQhhmead+mTRsjJ/p07do1TIB0TdOWUPMxY8YM2fiabVdNdLGkCMn+/fvlsCQmdjCMHTtW+oIqEVoteKwnoIwxjM5uNywrQsLAPgxxF53oWosXL0by5MnDBMhTgvWBLeaDJ3Vxp4QdliTCY2kR0lOibt268oz7V2H79u3PWEJpcbt2LfIDXjTugRHNCxYsaNn9gi/C0iIkx48fR+HChTF+/HgjJ2owkBT9UZUAeXwZN4dqzAV3SdBf12pRtV8Gy4uQLFu2TP6johqZ7c6dO3JoowSYLl06bNiwwbiqMQt0nmfEPbvP0W0hQsId+Jy4RyVOKU/LVQJkuMKZM2caVzRmglHY7eCg/SJsI0J1HiBP5bl7966R+1+4OVgJkMdX//DDD8YVjZngDolixYrJ7Up2xzYiJBy+0M2sRYsWEfp6cj9iihQpwkTYsmVLvTvehPAIBHor7dixw8ixN7YSIaEXDcMRdujQwch5Cv+hmTNnDhMgd+rfvHnTuKoxC5MmTZLzezu5pb0I24mQHDlyRHpW9OzZU75mD8m9Z0qA+fLlk1ZVjbmYPXs2cubMKdduPQlbipDQo6ZEiRJyDyLniUqAGTNmxJYtW4x3aczC0qVLkTt3bilET8O2IiQ7d+58JkIaf9eWUPNBn1DOATkU9URsLUL6hDIshRKh9gk1HyNGjJAC5M4YT8W2IqQl1PHseC8vL2k1dd2hLZrnwSMOevXqJZ3wPT14li1FSJ9Qzv2UALkTn7FDufhbqVIleba8xn3QY4nLQ5yz8//i6dhOhGfPnpWWUSVA+pUyNg3h2iG9ZQoVKmSLKF1WhMcZMEBTtWrVLHmWoDOwlQgZC6ZWrVphAozMEkpnb1ri+vXrJ2OLalwDjWIcfrZr1w43bhjnpmvsI0LutmfYAyXAJEmSYM6cOcbV/8KTXRnOnq2yHhI5FzaO/N9QgLSEap7FNiIcNmxYmAC5Sz4qB0YyrkzHjh1RoEABW+7YNgObNm1C+fLl5bzcrvsBo4stRDhv3jzZ8ykRMvbMywQI5gJxkSJF0LRpU+zZs8fI1USHy5cvy/CU9E769ttvtY/uc7C8CDnn4/KDEiDnhLdv3zauRp0TJ06gVatWcgc3K42es7wabPymT58uD9GpWbMmNm7caFzRRIalRcioW46749mbUUzRYc2aNdJyx82k7GG5nqWJGlwa4mZpLj34+fnZJjivs7G0CGlcUQLkiUkMhRATcCljzJgxcj8b/U6tfvSWs6GfbufOneXc+uuvv5ZH2WmijqVFSMNKnz595LBn1apVRm7MwfVFnlHPdUcGBuZpva44jMYqMBo2lxvYWHE+HdXwIppnsYVh5nk76WMCipG7MTjM4pwzICBAen14Iox8zXl48+bNZePEEJF8baeI2K7GFiJ0FRxm8bBSzkO5KXj06NFy76InQGsnF9s//PBDKT72gOwJNdFHi/AVoBM4z9Fnr8jNwjw6jUYcDo/tBAPtrl+/Xrr60VBFv1ue08g5oCbm0CKMBrT+0SLI9bCKFSvKRWme7stdAVY9L+H69evYtWuXdHZgMGRGsGNwZZ7ZqAMjOwctwhiCc0Run+Icib0GXeKaNWuGCRMmSCuumRer6VTN/XyMy8PlGQ63aRXmMoPe+uV8tAidAM/GYM/BRX+G6acoOYeki9zEiRNlT8m4N+4wZjC4FYNe0YeTxqY6derI8zxq1Kghe3H626pdJxrXoEXoZLjmSOMN54xcS2MPw2ErhUnncR50wsDFDPPOYSAPJeV2LBpCOMeMauBbOhWwN+bpRYw4x0BWdEyn88GoUaPkvI6BdPm5FB19OfnZbBToqqcjz7kPLUIXwyDFrPC0LHIIyJAbNOxwGEhxUCSMncq1T3qfNGnSREYE4C4EipjnKPbo0UP2Wl26dJG9K93tGPiYB2jSWMRet0KFCrI8Hx8fucbJe3i6MR2q2VPrM/jNgxahSaAlkksgPJSG6248X4NDRnrucFjLUBBKeOzV+JOvKa7+/fvLWC1Tp06VPSrP1WAveO7cOaevoWqijxahRuNmtAg1GjejRajRuBktQo3GzWgRajRuRotQo3EzWoQajVsB/g+9OyBxhaK9NwAAAABJRU5ErkJggg==)
A uniform disc of mass M and radius R is supported vertically by a pivot at its centre as shown. A small dense object of mass M is attached to the rim and raised to the highest point above the centre. The unstable system is then released. The angular speed of the system when the attached object passes directly beneath the pivot is
![](data:image/png;base64,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)
physics-General
physics-
A bar of mass M & length L is in pure translatory motion with its centre of mass velocity V. It collides with and sticks to a second identical bar which is initially at rest. (Assume that it becomes one composite bar of length 2 L ). The angular velocity of the composite bar will be.
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)
A bar of mass M & length L is in pure translatory motion with its centre of mass velocity V. It collides with and sticks to a second identical bar which is initially at rest. (Assume that it becomes one composite bar of length 2 L ). The angular velocity of the composite bar will be.
![](data:image/png;base64,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)
physics-General
physics-
A small particle of mass m and its restraining cord are spinning with an angular velocity
on the horizontal surface of a smooth disc as shown. The force F is slightly relaxed, r increases and
changes.
![](data:image/png;base64,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)
A small particle of mass m and its restraining cord are spinning with an angular velocity
on the horizontal surface of a smooth disc as shown. The force F is slightly relaxed, r increases and
changes.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQEAAACJCAYAAAAseI38AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AABpFSURBVHhe7Z0JuE5V28dNCUX66Cp8hpdX0xelMqXp7Wv0Jg0qChVJo6JRGjWg0kSiVKKZQtJkqogyJKXhFA3IlDJmiON+92+dfZ93eWzVCdd1nr3u33Wt63n22nuvvdZ61v1f415PETEMI2hMBAwjcEwEDCNwTASMLfh99TJZuHSFbJaNsmThQtkQ+xvpxUTAyCP3Vxnar4fc1ftJ+Wzectm4ab3MHjtYLr/iJvng2xXxRUYaMREwRDYulQc6/ltOvvhembtytbzRp7v0GflJJAxr5frj/in/6vSk/B5faqQPE4HgyZVxj7SXSrX/Xz5ZGR3+OFr23aO83PjyF+5sz9Nry/+1uFvWuCMjjZgIBE7uitly2gF7yL9vGeWOv3i+mxxy9Dny1aroYO3nckqtinJW95GRVBhpxUQgcJZMe0b+uUcVeXxmXl3/Vr+7pe+ome77V0O7SaWqh8nob6wdkGZMBAJn2ecvSt29a8uA6fNkQc7HclvHy2Xw5ByZ/82H0q7pv+SmpybGVxppxUQgEH7//Xe55ZZb5Kmnnop9YjYtl+H9uku3nn1l9IRpMufrmTJkQB954IEH5OV381oERroxEQiEefPmyS677CKNGzeWTZs2xb7/Jdfz27xhray3QYBgMBEIhO+++07Kly8vxx57rGzcuDH2/S+bN2+Wzblm+SFiIhAIP/zwg+y5555y3HHHSW6GsY8cOVKOPvpo6datW+xjhISJQCAsWbIkXwSUOXPmyMUXXyzFihWTIkWKSIcOHeIzRkiYCKSUDRs2yOTJk6V///5yxx13SMuWLZ2hIwQXXXSRXH755VK1alXnp65v375uANEICxOBlLFmzRrp3bu37LffflsYOI4xgd12220rf3UVKlSQGjVqyMsvvxyHZoSAiUDK6Nq1qzPoihUryoUXXigDBgyQESNGyKRJk2TmzJkyY8YMadq06VYCoI6WAmMERjiYCKQIRvhPPfVUZ8ynnXaajBs3LnEmAAYOHCjVq1ffQgCKFi0qgwYNiq8wQsFEIGVMnDhR6tSpk2/Y9Pvr1avnxIGWAeMBrVu3dsflypXbQgRq1qwpq1bx0oAREiYCKWTp0qVuZSBGf+CBB0rZsmW3MHZ19P9PPvlk6dixoxsrOPTQQ+MQjJAwEUg5q1evdtOD7733nuy+++5y+OGHy6xZs2T+/PmybNmy/NmA77//XhYsWOC+G2FhIhAIixYtcrV/w4YNYx/DyMNEIBCYOuzevbs888wzsU/6cEufI2cUDBMBI1UwHnLzzTe7AVLjr2EiEAg//fSTnHnmmYlTgLxLsG7dulTUop9++qnr9rAc2vhrmAgEwuzZs51xIAQ+c+fOde8MMG34yy+/xL47h8wXl7aHb7/91nVv3n333dgnDwY9S5QoIRdccEHsY/wZJgKB8NVXX0mpUqXk3HPPdcfr16+Xxx57zE0TIg6HHHKIm0nYkfD+wvLly90bjLystCNF4J133nHxLlOmjFx11VXuVWlA7Ng3gfUQxl/DRCAQEAHWApx//vny4YcfyoknnuiMSN39998fX7njYMUiKxfZ0eiRRx6JfXcMdF14I1LjX7t2bXnhhRdcd2DXXXc1ESgAJgKB8OWXX7r3CUqXLu3WC/gCwHLhBg0aOKNi05HtcUceeaS0aNHCTUkiPExJYpi0CnJyctyeBVdffbV06dJlu9z111/vwibumg5eiWYdBH6XXHJJnHLjzzARCIRvvvnGLQs+4IAD3EtCvggUL17cdQfq168vhx122N92rDgknFatWrmFR7iTTjrJbW0Go0ePdqsXqanpmmyPQ8xY9uyLgDr8Lr30UvdM488xEQgEXiT6+uuvZcWKFW76jFrUNxy6A1xDjb09jrEGhZbAUUcd5QQI2Nvw119/dQOQfG6PY6wBQ/fTgAj16NHDdXvatWvnnmn8OSYCgYABMk24du1ad4wh0TRnYA0DOuKII7Yw4B3BlClTpH379vL+++/HPjsOljzXqlXLxZ3ZAN5/YI0AA5A2MFgwTAQCAeOoUqWKdO7cOfbJgym2Jk2aOBFYvHhx7Ltj0NmAHTkroLz11ltOAPbff/8tNkFhitBEoGCYCAQCA4MlS5aUM844I/bJG2EHXh/++eefs2qxEPFl8xMdb1AYhGRMoE2bNrGP8WeYCAQC/XMG084555zYJ52wToCBQ2YgFHuf4I8xEQgEFYGzzz479kknv/32m7z99ttugRIDkAwgGn+MiUAgfPHFF24q0O8OpA2t8ZnluO222+SYY45xax8eeuihbW6zZpgIBAMzAyzmYalwmiGdTA+yaAnBY8Bzr732couLbDv1ZEwEAoER+hBqQ/5IlSXR1157rZx33nlu+7S6deu6hUUsVjK2xkQgEHhVmA1Fpk2bFvukD9ZAsGT5uuuucwODiAArFllKzH8u8PKUtQa2xkQgED777DO3ZJc/JaFLgCCwGWlaHOm58847neHfe++9cuWVV+aLAEuaK1eu7LZYt30Ut8ZEIBBGjRqVv7wWxzQaK+0YLNTPpHX42eKIO+8k8Ocr99xzzxYiQEuArdd5cWro0KFxjhiKiUBKodnLdBlNZBYDff755+7/BzGYtm3byvPPP+/6yK+//roTCFbgjRkzRsaOHZu1jtekb7/9drfZSKYI6B+tcN6HpdLkEVOJLK1mWnFnrHAszJgIpBBGyNlogxrx0UcfdX1h/oPgpZdecq/bsusOi4b4o9Jnn31WHnzwQVeD8gJQNsPegqTjj0SAcz5PP/20G0xkz4PBgwe7z2HDhsVnw8BEIGWsXLlS7rrrLnn44YfdbjsvvviiNG/e3BXuN9980xkCA2dMo1FzsoiI9/wRDMSAAcRshXTxUlRBWgK9evVy6UYMOffqq6/KDTfcEJ8NAxOBFKDNV14Suummm1xBBroDDJLxxyN9+vTJ35KLhTTUgE888YTrFij43X333e4NvWzkxhtvdEKACGaKQLVq1dyLRYijDwuJSDd5dt9997k8Ig8hlOXGJgIpYfr06W5BjP/aLoZPv59/IOLvyunza23IvxVj7Bg9240pw4cPdzUhXYpsg9qcbk/SwCBvUO6zzz5ulkRBPMmXfv36uXsRgVdeecWJAGMFJgJG1sDgHrUgm4Yo7O9HoQYMmnnzJ598Mn9MgOk0oMtAXxqhUD744AO32OaTTz6JfbID3hdo1qyZG+tgTMQXAVYNsnrQ/8NVRGDhwoUuf9RxzDRito+PFAQTgSyGQkxTliY/r9Yq7O9Hbaav2bLZxvHHHy+33nqrm0bDUNiVRxfOUPsxgOhDjUkYO2NDkJ0JA4O8RoyIsc2ZigCbp6R9yfTfpVCIAAWOwjxkyBDXR33uuedc84xPdfhz3vfDscMs/pnnuJ7RXg1H7+fPN/QZ6rgu088PT8Pyz+NH2HofnyxY0fv0HuLHpz5Dj7mG+9WfY+7V7/hr+LjM9A0cOND1fSnYfq2FMLBVGH1bhTSzOSddA7oDtAIYFBwxYoQ7z3Linj17uhaADzUjtSr95qR807j5+UA8iTvpxE/Tqun2/f3vfPrf/WcQPteqn4bpX4cfm4swJnDwwQe7VgBicMopp7jxgEqVKrl8YYYkMyw/HN/fvy7zXGYc/Tjp+R29hfvOolCIAG+4USAZvWbOmp1i6c8yd03B5dVQajGavOqH43oGdOgHMq3DsZ7jHvrI1AzcwzGFn74ix1zLJ81G9qVTP354Cg+1o17Tt29ft02Wfx9xYcRd/Vi1xh94EH+e1alTJ1foOGZeHuPQdDAwxzHPIf7s7oOR0lcnPK7jHkatOcYASSPfSSe75pAu4gh80hQG0o7RKgwWYvCkkVodEWAcgLhfccUV+d2AH3/80YWJ4QPdBMYHmC0gHeQbBkbcSC9GRmHnmK4Go+zEj40+mHlg0JFjpt9odZBGame9TsPEn/iQn4TFfdzPM3D40SIhz7gPhyjwD0OvvfZa/u+BAZJHb7zxhhODpk2bun0U69SpI2eddZb7HShj3Ee8NXzymfzlu5YdjR+/Id/VH0f6SDtx0Hu4BhElP4kvceCcbuVW2Cl03QEWbVBQMtd4M5DFnnWZML3FwE4SCAmbTChMl/nNWxaHMIjEn3UqhOcbEWAM/LA+FBL+zluhFqVwKTTRqQn4hx+/qU3NzcabLN7p379/7Jvnz7OB2pz7NV707xEnwEh5toKxIm5sIEp8GNSjXwvkIeMCxB2DY2ScEXL2FKAVgVHgx/OA1gNGS8uArcYQJe1mkA4/XxhfYDASpk6d6lomCqvyMDpghoLBN+LC74fBAekgjYCAIXjAb8IUnz8oRyWR2V0hDzKXACN0dIWAPKB1iZH7sx3kOfFV+M2S/reQ+xGnJLgns5tEPpHObHxJq9CJAAUeg/chgzFW/YF9MA5qhEyo2VBnNSSazBiLH8bkyZO3+lOMxx9/3MVBoVDSJPa3scJYKXD+xpwUUm1O85KOGgzCo3vgEQYFnxoCo1dRIzyMkmcBtaMaFcbDOebzgWamn14MjloQCNsvnJyjxmLtADUjcWaLMRYK0doiHhi9dh0wPIyLgUYgbyZMmOC+g58PGA4iC/w+KkSAyCHk2k0hb5iBQFgwLJ6rAoW4kG7fgBH1SZMmue9AuAiDb8y0fmja+5DPmcuCeZ62boD0+JUG8Ur6YxRtASFAmSAiKlqggkUaEPdso9CIgGYkapr5phs/FIU1E4wQf/bPy0TnxhV+TH4kH35832gonBQ2v4ZhvCJT4TE6nYsHdu7FALWQ0jVQQ6Kg66g9TUWMmxYChk0tCXQNaGYqdD+0duL5WjtTY2Nc7KMH5BlCN3/+fFer++mlMFKTk0cIDi2E8ePH53cHGDRDoIgz3QDCAAYRWXCDQZKHfg2PoND8Bc6TVwgM8aCGVcHgmPTpVuO+oZEfM2fOdN/JJ00332lWA5/E2YfwEUcFkUd4/PEQ8or88EEY/BWA5D1dIe2vI0xUMKQ7EwQ3afUgMwykT/NMIS3kabZRqFoCNMH4QTK3hGLATQufD81ICrrWoD70LX0DpwD7Nai2Lvwf/6OPPnI1uDaPKcwYqG/wugBH++BAsxjjBISE89Q+PIP4qcARNoLAfD1pAuJOgdKuhd6jLRgKsRYsnslz9ByGQG1FKwHD1ZqYOBIGwofTuXPW1yMC1OgIAX1eCjItH79moxYmXPIGQ9MWz8cff+wEkfSQRxi2tmYIgzxXqKW1ptaanHCowbVlRI2q4sBvpYaPCGPMCIyCAPjdJ/KNOM+YMSP2yTNw8l67Q8A0J2nR3wBoCWirDX/SRKswE+71u0s+tBj9wVdg/IW8zTYKlQiQqRhdJhRYvymoULOi1pnQ1NRaSqE21T43UDvxQ/pgmISpYEyEQ02vYMQUKh9aBhg2UANr/xXD0KY6tQfpoEDxXG3tEJ7f36W29mtfnqVNcGpmakyFsQpqKsTFn9PnGkSPWhIxoGblGaQNEaAm5BqEVdPCp983pktGa4ZPzTcdr1Hh5H41dJ5F+hBBQLAwSIW8JXxe0NHamrwgfuQzwkZLTQWO+PjrHhAS7vOXNfP8zN+fsQo/Hdrl8bsEGLz/2/Pb6e+UCb+/v7ZAIU8yywHlDkHJtteVC4UIULjIVBat0KylVkRVKUgUXEalOc8gGP44akFG1Kml9Xq9B+NgtJm/r+YcxnPNNde4QkUYOGpfDIXzOParv+yyy1xTlfOEQ/OOZjTPou+KHwWRGonvXEeTl0E3Ch7XURMQLobLqDa1OLUttSQFhFYDo8gMWHI/BkyNxr0c8zwMm2Pizf8EkC7iSNiMgfBs8kP/149aXo0DEWIGAgNjYIy8wGiJN0aDCJDPdDkwXIycPOYaugUqtqSXdBEfamjig+OZGAxxoPnPiD95QHoZwSe9nCOvmZ2h9cE5xJ1WhYaLIeJPmrgHI+V3Rnh4DqJFHAlL857fm7iSF+QVrQfyh5aQ/maIG2LEMY5nkF6eoffReiDfaMXgR4VAnCgvnPfLEiKgea7+XMPvRxikQ88Rb55NS4Nws2WQsFCIAM1PCjKGS2FFuek7YjQUEmou9VPHOYyM2sY/hz+FEUPgO+f4IbkWY+MaFJxnUfNwnmPC4Rru4Rr8CYfna/ic4z59JvcRX+6jhsSgMRrC5TtGRaGgScl3hEevJy6EQQEl7YRNeJzjfo55NjWlPotreTbneB4GyHQaxkN4GDWGRoFk3IBnUzshQjyf7hDv3TPdSViAAPOdbggCjFjRRNYpxA4dOjjD55k8g/iQLxon8oO4cMyz/XznPtLAfVxDHPjEn7zgOu7hmPziXo7xJ+5cTzj+76q/B8/mk/wmT/WYcEkP13MfzyYtfj7yLPKZZ+CH41jD4T4tA1zD/Rqefw5/4st3/LiG+JEenqvds8JOoRAB+ncUVkA9Kcwc88k5CiXHvuMccF6vV39qQb1HwwD/OvDvVdXW8344eg2fkPlM0HiDnve/Ew7hZT5H/TU80LC41087aHhcw3ccNRiFj6krRsfpG1MQqbGAWpWWEN0CWgIUeJYOaxeCbgsFmXggQPT9MSbEg/A1Pn46/PjyyTH+/jmu1fjyqdeChunfk3k9xxpW5nn8NCz97t/n+3HsxwsHGgc91nO+y0yT78CPj/8sjvmeDRSqMQHj70E/m511qWWBZrSOatPNYa6c1hCDa4gA32n+0pLQQT9qLsSA/iwCQg1L68BIPyYCWYzWNBguO+xSc2stTk1Ec5TvjAUwfagDgzS7GXxELHTmgakymrd0DxgL4V0DHaQz0o2JQBajTU9qdpbmMspOf5iBKmCknO4Bg370Wf3ZAUbHmUqjG6GrKmkJ0F9GQFhq7E+xGunFRCDLoTnPLAD9fAxbpyqZg8fAMWhGrX0RoLlPy4A+MQtsEAVqfUSFeXumahnZ17CMdGMikMVod4AmPK/M0rwHBgYZDdclrAwQJomANveZw9d5clYCMirPdCljDUb6MRFIAczTn3766U4MgHUKuioPmINn6ksHBhkTYO6f0WygS8GsgC4KYs3DCSec4MTESD8mAlkOBoyBs1EI03yMCWDAtASY98bRtG/ZsqVbSMNbhPT3eZOQsQSd4+cVW/69BzFgLQJh+C/xGOnFRCDLQQRYnUdtj2NFIu8LMOjHajkc51kJyRJbFgvRHeClK1oQrDHgkxVutABYZMQKPc7rOgMj3ZgIJECzmFdtW7ZqKee3bl2oXes2baRd+/ZyUbt2brOR9lGNjuM7fiwKopZnaS37CtAdYKkw3YVGjRpJg4YN813jI46QhrFfo8aNpX6DBnJIvXpS79BDC7GL4xfFU1/KMgqGiUACTJNhLGlyzB7oq8SMGfBmYeY12e46duwY/4JGQTARSKBH1I+mUFUsUlSqFikulbPUVYlcxSLFXFp4+YYXfviOCFwSGQzfqxQtJtWKFZEaUTch21y1oiWkZpFdpFLR4i4tvOtgFBwTgQR63nefK1QUrlqREdWIxABX3XNJfts65x9v69y2/LZ1zj/e1rl/RK5SlA7SwktGSSLwv1H6akaf1bPQVYtErmaREk7wnAhceWX8CxoFwUQgARWBvYoVl+pRTVk1+p6Nrlrk9o7cViIwKBKBS/NEoFIkAv+IPpPuL+yuSix2e0etAhOBv4+JQAIqAntHLYGakZEk1ULZ4GpEbp/I/ZEIVMnilgBCQNwrFc1Lo4nA38NEIAEVgX3yuwN5BpVtjho+sTvgiQDdgVrRZ9L9hd3R0iHulU0EtgsTgQTu7dHDFapykWNwsEL0ma2ONJAWdsHR2QGm0phC5HvJyJWJXNnIcW02ud0iR7xLR460MM5hFBwTgQRYVFOiRN5gU1ocuxfpsmHWCbCDEP/PV7ZcOSm7xx5Svnz2uT2jeP8PcY/SUKFCBbfy0Sg4JgIJ/LZ6jYwcPlwGPfusDIkE4bksdoOHDHE7/LJZKvsEIAL699ysLGSH5WnTp8vULHTTp0WO71OnupWOusmpUTBMBAKCPQZ9ETAMMBEICBMBIwkTgYAwETCSMBEICBMBIwkTgYAwETCSMBEICBMBIwkTgYAwETCSMBEICBMBIwkTgYAwETCSMBEICBMBIwkTgYAwETCSMBEICBMBIwkTgYAwETCSMBEICBMBIwkTgYAwETCSMBEICBMBIwkTgYAwETCSMBEICBMBIwkTgYAwETCSMBEICBMBIwkTgYDgn4gRgd69e8c+hmEiEBSTJk2SJk2ayLBhw2IfwzARCI4xY8ZI69atZf78+bGPETomAoHRqVMn1yVADAwDTAQCo3Pnzk4Exo4dG/sYoWMiEBhdunRxIjBu3LjYxwgdE4HAMBEwMjERCAwTASMTE4HAMBEwMjERCAwTASMTE4HAMBEwMjERCAwVgfHjx8c+RuiYCATA4sWL81cIdu3a1YnAlClTJDc3V+bOnSs5OTnuuxEmJgIpZ+nSpXLQQQdJmTJlpFWrVu7dAUSgbdu20rx5cyldurSUKlVKFi1aFN9hhIaJQMpZt26dtGjRwhn+tlyzZs3cdUaYmAgEAK2B+vXrb1MAVq1aFV9phIiJQCDMmjVLKleuvIUANGrUyLoBholASIwaNUpKlizpBGDfffeVOXPmxGeMkDERCIxevXpJ3bp1ZeLEibGPETomAgGyYuXK+JthmAgEw7qVv8iCBQvcmoGlixbJ0uVr4jNG6JgIBMIvnw2XFiefKg++NkHefOlxeWLo+7Le1gcZESYCofDrNLn47DYyfnH0ff0yWbx8rWwyETAiTARCYfkM6XDaqXJH30HS75EB8qX1BowYE4FQWDFDOrZoJc9NzpGc2bNlydrY3wgeE4FCwWbZsDF3pzbPN8wbI82PPUmG5tjyYGNLTAQKBbmyZMV6WbUhPtwJ/PzlBOnerZu8Pm1e7FMwNsefRvowETCMwDERMIzAMREwjMAxETCMwDERMIzAMREwjMAxETCMwDERMIzAMREwjMAxETCMwDERMIzAMREwjKAR+Q/261TQMlwZXgAAAABJRU5ErkJggg==)
physics-General
physics-
A small bead of mass m moving with velocity v gets threaded on a stationary semicircular ring of mass m and radius R kept on a horizontal table. The ring can freely rotate abut its centre. The bead comes to rest relative to the ring. What will be the final angular velocity of the system?
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lzVtzdGYS6HgVRxLcXlsY5TzhKa2IUbI+IMTNSrmPVwBow5CuJRu+u/1MzpanHp6G1V2EUKh2A2Rdsk43ZERAx6oOIMTOMLePOQFPL+FoYsu2lGknaHog6HgVQuFIfrHKiZDoiRn0QMWbKA8RsGoWaxjGgZ90BWJVtepAkbHu/BdyNY8xKPebh0n3nGU+JGPVBxJgF9xNP4IsejITujiZDF+BYpgl87yFyzVi0LGuAwbMpgrfFOpVljohRH0SM2ZB49nu8F1BFCbL2y8MweeFGHDz9G+Ku30Bc9Fkc2rYCU0f2RH3vfDC4+2PgrD24lVfXNTJBxKgPIsY/we/Rv2DRh2+gRY0y8Cjpjao1a6Ouvz/q/uMpVC3vjTI+1dGsx0jM33zS6YRIRIz6IGL8s6Ql4HLkEezauBzzpoeoEIwTp8zE18t/wO7DpxF103lmTzMiYtQHEePfxNriuLMiYtQHEaOQLSJGfRAxCtkiYtQHEaOQLSJGfRAxCtkiYtQHEaOQLSJGfRAxCtkiYtQHEaOQLSJGfRAxCtkiYtQHEaOQLSJGfRAxCtmSczE+xL2kRCQlZRXOMg0piYn4PTnVaUJe/lVEjEK22KJljFoTjD6dOuKN/2zH7Yz+ZWkx2D5nOF56vh+mhUfCea18s0bEKGSLLcSYcGIW2pU2wFC+I8LOp4+CkHDyW/SvZtxXoQtC993Ks5H1coqIUcgW24wZE7BtdAuUKFQKzwbvQrJpKxCH7VM6ws1QCu2DN+C6q/ZRjYgYhWyx1QRO8vkwdKlYBCVrv4bvYh5tu3tuLd6uWwgGv35YcMxVO6iPEDEK2WIrMSItHj++3xTFilVEl5mnjRsSsD+0F0obPPHCmHWIc9X+qQkRo5AtNhOjkcTIBejsUwy+bYMQfmwnxjYrDEPNXvjyiKQKEDEK2WJLMSL1Bjb+uxm8fKqjTa9uqFnIC21HfZ9l6gRXQcQoZEu3bt2watUq0185Jz5iIXr4PspyVaBmD8w57NpjRQ0Ro2CV2NhYldefWaiaNGmCcePGITIy0jaZp5LjsP0/fdCyxQsY9MkGaRVNiBiFdDCF+LJly1TmKU9PT9V6sTB5KtPBjR49GqdOnTLVFmyJiFEww9TgISEhKm+/JkJrpWnTpjhx4oTpU4KtEDEKZjZs2IBSpUqZRVerVi306dMHAwYMUIlTmbFY29e1a1fJ629jRIyCgmPBUaNGmcXWoUMH7Nu3zxySMi4uDgsXLoSXl5faT9FGRESofYJtEDEKiqSkJJWRWBPjm2+++Vgy1IMHD6oc/9zPVOP8W7AdIkZBwRYwLCxMTdRQbJy8efnllxEUFITJkydj2LBh8PPzM+/nuDE+Pt70acEWiBgFMxRX3759za2jVgoUKJDu79KlS2PdunWmTwm2QsQopOPq1atqTdHb2zudALXy3HPPITw83KXSG+iFiFF4DE7mnDx5EkuXLlXCDAwMxNSpU7Fjxw5cvnzZVEuwNSJGIUsozJSUFGkJdUDEKAgOgohREBwEEaMgOAgiRkFwEESMrsyDJJzatAhhy7YiMi4Kh7aswtezpmHa5/OxLHw/LiUY66TF48yeDQibMxPTZ4RiyfpdiIgRm1R7IGJ0Ze5GI7RLeRT1fAovvdYdrZo0QqOmzVCvehkUKeqD596ehMnBI9C9VUM0atIMDWv7okhBT/j3mISfrqYPtyjkHBGjK3M3Fgv6VoLBkB/lGvfH/K0RiEtIRMzRb/F/z5ZTi/we/r0RsnofouMTcP38LnzcqRoK5fdC7wUXXDbyt70QMboyRjF+3bsc8rtVRb8vo00byTWsDw5AUYMbOn22C3dMW8lvc7rDx8MdzcfscdnI3/ZCxOjK3I3Blz3Lomg5fwRusWznrmLdR+3hZqiCwYsP4Y8R4kP8Nr83fDxLGsW4W8RoY0SMrowSow+K+TTAmO2ppo0kFmuNLWMJQ2UMCjuIJNNWivHSvF5KjC3G/ixitDEiRlfGQoxB20SMuY2I0ZUxinF+d28U9vbH6K3pxbhmfDvjmNEXb35zIL0Y5/aAt5s7/idIuqm2RsToyqiWsZxxzGi9ZSxuqGS1ZSzn4Sktox0QMabjITJEmtAR43eb/qcbD+8j/vJZRJ69iGtJlt9+H4nXoxB5+hxibyenS9GWGn8ZZ8+cwaXrd/U/X6fl0XMnYrTgQeI1xN1Kwj3dvYUeIuX2ddxIvCcPuAvyICEOV27ew38B1hxeXQbxL9kAAAAASUVORK5CYII=)
A small bead of mass m moving with velocity v gets threaded on a stationary semicircular ring of mass m and radius R kept on a horizontal table. The ring can freely rotate abut its centre. The bead comes to rest relative to the ring. What will be the final angular velocity of the system?
![](data:image/png;base64,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)
physics-General
physics-
A uniform 50 kg pole ABC is balanced in the vertical position. A 500 N horizontal force is suddenly applied at B as shown in fig. If the coefficient of kinetic friction between pole and surface is 0.3. The initial acceleration of point
is
![](data:image/png;base64,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)
A uniform 50 kg pole ABC is balanced in the vertical position. A 500 N horizontal force is suddenly applied at B as shown in fig. If the coefficient of kinetic friction between pole and surface is 0.3. The initial acceleration of point
is
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)
physics-General