Chemistry-
General
Easy
Question
Equilibrium constant of some reactions are given as under
The correct answer is: ![y not stretchy rightwards harpoon over leftwards harpoon zK equals 2 cross times 10 to the power of negative 2 end exponent](data:image/png;base64,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)
Related Questions to study
physics-
Two concentric shells of masses
and
are having radii
and
. Which of the following is the correct expression for the gravitational field at a distance r :–
![](data:image/png;base64,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)
Two concentric shells of masses
and
are having radii
and
. Which of the following is the correct expression for the gravitational field at a distance r :–
![](data:image/png;base64,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)
physics-General
physics-
Potential energy and kinetic energy of a two-particle system are shown by KE and PE. respectively in figure. This system is bound at :
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)
Potential energy and kinetic energy of a two-particle system are shown by KE and PE. respectively in figure. This system is bound at :
![](data:image/png;base64,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)
physics-General
physics-
Find the distance between centre of gravity and centre of mass of a two-particle system attached to the ends of a light rod. Each particle has same mass. Length of the rod is R, where R is the radius of Earth
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)
Find the distance between centre of gravity and centre of mass of a two-particle system attached to the ends of a light rod. Each particle has same mass. Length of the rod is R, where R is the radius of Earth
![](data:image/png;base64,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)
physics-General
physics-
A bicycle has pedal rods of length 16 cm connected to a sprocketed disc of radius 10 cm. The bicycle wheels are 70 cm in diameter and the chain runs over a gear of radius 4 cm. The speed of the cycle is constant and the cyclist applies 100 N force that is always perpendicular to the pedal rod, as shown in the figure. Assume tension in the lower part of chain is negligible. The cyclist is peddling at a constant rate of two revolutions per second. Assume that the force applied by other foot is zero when one foot is exerting 100 N force. Neglect friction within cycle parts & the rolling friction. The net force of the friction on the rear wheel due to the road is :
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)
A bicycle has pedal rods of length 16 cm connected to a sprocketed disc of radius 10 cm. The bicycle wheels are 70 cm in diameter and the chain runs over a gear of radius 4 cm. The speed of the cycle is constant and the cyclist applies 100 N force that is always perpendicular to the pedal rod, as shown in the figure. Assume tension in the lower part of chain is negligible. The cyclist is peddling at a constant rate of two revolutions per second. Assume that the force applied by other foot is zero when one foot is exerting 100 N force. Neglect friction within cycle parts & the rolling friction. The net force of the friction on the rear wheel due to the road is :
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)
physics-General
chemistry-
In a mixture of A and B, components show negative deviation when -
In a mixture of A and B, components show negative deviation when -
chemistry-General
physics-
A bicycle has pedal rods of length 16 cm connected to a sprocketed disc of radius 10 cm. The bicycle wheels are 70 cm in diameter and the chain runs over a gear of radius 4 cm. The speed of the cycle is constant and the cyclist applies 100 N force that is always perpendicular to the pedal rod, as shown in the figure. Assume tension in the lower part of chain is negligible. The cyclist is peddling at a constant rate of two revolutions per second. Assume that the force applied by other foot is zero when one foot is exerting 100 N force. Neglect friction within cycle parts & the rolling friction. The speed of the bicycle is
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)
A bicycle has pedal rods of length 16 cm connected to a sprocketed disc of radius 10 cm. The bicycle wheels are 70 cm in diameter and the chain runs over a gear of radius 4 cm. The speed of the cycle is constant and the cyclist applies 100 N force that is always perpendicular to the pedal rod, as shown in the figure. Assume tension in the lower part of chain is negligible. The cyclist is peddling at a constant rate of two revolutions per second. Assume that the force applied by other foot is zero when one foot is exerting 100 N force. Neglect friction within cycle parts & the rolling friction. The speed of the bicycle is
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)
physics-General
physics-
A bicycle has pedal rods of length 16 cm connected to a sprocketed disc of radius 10 cm. The bicycle wheels are 70 cm in diameter and the chain runs over a gear of radius 4 cm. The speed of the cycle is constant and the cyclist applies 100 N force that is always perpendicular to the pedal rod, as shown in the figure. Assume tension in the lower part of chain is negligible. The cyclist is peddling at a constant rate of two revolutions per second. Assume that the force applied by other foot is zero when one foot is exerting 100 N force. Neglect friction within cycle parts & the rolling friction. The power delivered by the cyclist is equal to
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)
A bicycle has pedal rods of length 16 cm connected to a sprocketed disc of radius 10 cm. The bicycle wheels are 70 cm in diameter and the chain runs over a gear of radius 4 cm. The speed of the cycle is constant and the cyclist applies 100 N force that is always perpendicular to the pedal rod, as shown in the figure. Assume tension in the lower part of chain is negligible. The cyclist is peddling at a constant rate of two revolutions per second. Assume that the force applied by other foot is zero when one foot is exerting 100 N force. Neglect friction within cycle parts & the rolling friction. The power delivered by the cyclist is equal to
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)
physics-General
physics-
A bicycle has pedal rods of length 16 cm connected to a sprocketed disc of radius 10 cm. The bicycle wheels are 70 cm in diameter and the chain runs over a gear of radius 4 cm. The speed of the cycle is constant and the cyclist applies 100 N force that is always perpendicular to the pedal rod, as shown in the figure. Assume tension in the lower part of chain is negligible. The cyclist is peddling at a constant rate of two revolutions per second. Assume that the force applied by other foot is zero when one foot is exerting 100 N force. Neglect friction within cycle parts & the rolling friction. Net torque on the rear wheel of the bicycle is equal to
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)
A bicycle has pedal rods of length 16 cm connected to a sprocketed disc of radius 10 cm. The bicycle wheels are 70 cm in diameter and the chain runs over a gear of radius 4 cm. The speed of the cycle is constant and the cyclist applies 100 N force that is always perpendicular to the pedal rod, as shown in the figure. Assume tension in the lower part of chain is negligible. The cyclist is peddling at a constant rate of two revolutions per second. Assume that the force applied by other foot is zero when one foot is exerting 100 N force. Neglect friction within cycle parts & the rolling friction. Net torque on the rear wheel of the bicycle is equal to
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)
physics-General
physics-
A bicycle has pedal rods of length 16 cm connected to a sprocketed disc of radius 10 cm. The bicycle wheels are 70 cm in diameter and the chain runs over a gear of radius 4 cm. The speed of the cycle is constant, and the cyclist applies 100 N force that is always perpendicular to the pedal rod, as shown in the figure. Assume tension in the lower part of chain is negligible. The cyclist is peddling at a constant rate of two revolutions per second. Assume that the force applied by other foot is zero when one foot is exerting 100 N force. Neglect friction within cycle parts & the rolling friction. The tension in the upper portion of the chain is equal to
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)
A bicycle has pedal rods of length 16 cm connected to a sprocketed disc of radius 10 cm. The bicycle wheels are 70 cm in diameter and the chain runs over a gear of radius 4 cm. The speed of the cycle is constant, and the cyclist applies 100 N force that is always perpendicular to the pedal rod, as shown in the figure. Assume tension in the lower part of chain is negligible. The cyclist is peddling at a constant rate of two revolutions per second. Assume that the force applied by other foot is zero when one foot is exerting 100 N force. Neglect friction within cycle parts & the rolling friction. The tension in the upper portion of the chain is equal to
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)
physics-General
physics-
A uniform bar of length 6 a & mass 8m lies on a smooth horizontal table. Two-point masses m & 2 m moving in the same horizontal plane with speeds 2 v and v respectively strike the bar as shown in the figure & stick to the bar after collision. Total kinetic energy of the system, just after the collision is
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)
A uniform bar of length 6 a & mass 8m lies on a smooth horizontal table. Two-point masses m & 2 m moving in the same horizontal plane with speeds 2 v and v respectively strike the bar as shown in the figure & stick to the bar after collision. Total kinetic energy of the system, just after the collision is
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)
physics-General
physics-
A uniform bar of length 6 a & mass 8m lies on a smooth horizontal table. Two-point masses m & 2 m moving in the same horizontal plane with speeds 2 v and v respectively strike the bar as shown in the figure & stick to the bar after collision. Angular velocity of the rod about centre of mass of the system is
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)
A uniform bar of length 6 a & mass 8m lies on a smooth horizontal table. Two-point masses m & 2 m moving in the same horizontal plane with speeds 2 v and v respectively strike the bar as shown in the figure & stick to the bar after collision. Angular velocity of the rod about centre of mass of the system is
![](data:image/png;base64,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)
physics-General
physics-
A uniform bar of length 6 a & mass 8m lies on a smooth horizontal table. Two-point masses m & 2 m moving in the same horizontal plane with speeds 2 v and v respectively strike the bar as shown in the figure & stick to the bar after collision. Velocity of the centre of mass of the system is
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)
A uniform bar of length 6 a & mass 8m lies on a smooth horizontal table. Two-point masses m & 2 m moving in the same horizontal plane with speeds 2 v and v respectively strike the bar as shown in the figure & stick to the bar after collision. Velocity of the centre of mass of the system is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANYAAAC0CAYAAADo39J/AAAfuElEQVR4nO3dd0DU9R/H8eexkaGicIgabkVcqVgucFXuhStHWb9ya2m5LbMyK3Pl3rkRcOEWt6i4zb23qIADZBwHd5/fH9TlBc7ue8f4PP7Cz/f7vc/7e/Liuz9flRBCIEmSSVlZugBJyolksCRJATJYkqQAGSxJUoAMliQpQAZLkhQggyVJCpDBkiQFyGBJkgJksCRJATJYkqQAG0sXkFVdv3aNfXv3EBcXR81atahW3Q+VSmXpsqRsQgbrX9LS0vj155+YO2smz96fXNc/gElTp1GwoLsFq5OyC1VuuLv9XlQUB/ZHcOzoEapWq46HWo1/QL1M5x0+5GtWLFtKm8B2fNajF7a2NhzYH8F334yiQaP3mP/HYrnlkl4qxwcrZGUQ344cQXJyklG7f736TJ46DTe3AkbtbVo05crlyxw6fpI8eZwM7T0+7c62rVtYu2ETVd6umqEfnU6HtbX1K7dLOVuOPnlx+FAkgwd9iVarxbOQF25uBShSpCjOzi7s3b2LwYMGZlim44dd+Lxnb6NQAVSsXBmAK5cvA3DyxHGGfDWQE8ePMXBAPyqXL0u71i1ZungRer2eib/9StdOHajkU4aBA/px88YN5VdYyjJy9BareeP3OXP6FKVKlzEKihCCa1evkJiYwKq166nm5/fCz9Hr9TRuVJ9LFy9y6vwlXF1d2bg+jP59euHm5oZvhYo4OjoSsW8vCQkJvFuzFufOnaVWrdoA7Nq5g8pV3iZ49VpF11fKOnLsyYvHjx5x5vQpnJ1dMmx9VCoVrnnzkpiYwKNHj176WSErg7h08SKdu3bD1dXV0K7X66lZuw5TZ8wC4EDEPjp3bM/58+dYvjKUChUrAjBi6GCWL13Ck8ePyZc/vwnXUsqqcuyu4I0b1wGws7P7T5+ze9dOvv/uWwLq1+f7seMyTB8wcJDh5+IlSgLQoGEjQ6gAihUvAcCpU3/+p1qk7CPHBsu3QkVcXFx4+jQenU6XYXqqVguAtU3mJxYePoyl5/8+oXvXztSr34DxEydjY2O8gbe1taV06TKvXFNaauprrIGUneXYYNnZ2fFZj16kpqZy+9YNdLo0w7S4J094+DAWdw8P/Gq8k2FZIQRDvx7E1i2b6dDpQ6ZMm4GHh9qc5UvZXI49xgLo038AERF7OXLoEBcvnMfJyZmUFA0ajQZ7e3smTP4dFxcXo2WEEEwY/wv79uxh5tz5NGnazELVS9lZjt1iQfquWlDIaoaOGEm+fPmJi3sCQING77E5fGemF4mnTJzAtCmTGTZylAyV9MZy9BYLwNramt59+9Ozd19uXL9OkaJFn3tC486d20yZNAGA4KAVrAoJyTBPl24f8WGXrorWLGV/OT5Yf7OysqJEyZIvnEelUtGjV58XzlO06FsAlChZis979jaa5uTsTM/efY3OCAJUrlKFnr37UtTb+w0ql7KjHH2BWJIsJUcfY0mSpchgSZICclWwihX2pFhhT0uXIeUCuSpYkmQuMliSpAAZLElSgAyWJClABkuSFCCDJUkKkMGSJAVk22ClpqZyYH8EFy+czzAtISGBA/sjuHH9ugUqk6RsHCwbGxtGjxrJZ598zL9vdwwOWkHnDu24ePGChaqTcrtsGyyVSkWHTh9y+9YtLl+6aGgXQrByxTIKFChIg4aNLFihlJtl22ABtAkMxNramm1btxrazpw+xcULF2gTGIitra0Fq5Nys2wdrIIF3WnQsBHbt/0TrOCgFQC079jJUmVJUvYOFkCHTp05eeI40dHRaJKTWbdmNRUrVaZsOR9LlyblYtn+CeJ6DRpQoEBBNm0Iw8XFlfj4eLm1kiwu2wfL1taWtu3aMWvGdIoWfQs7OztatW5j6bKkXC7b7wpC+vHU/Xv3OHL4EB80aUrefPksXZKUy+WIYJUpW47adevi5laAjp06W7ocScpdg8n8/fTwjbv3LVyJlNPliC2WJGU12f7kRVYjhGD9urXcunXL0FazZq2XvoNLyllksEzo7t07DPv6K/bt3QOAq2v66X+ALwZ9xZeDvpbvL84l5K6giRw8sJ8PGtTj2tWrjBj1LfsiD3P0zzNMmT6TatX9mDJxApMmjLd0mZKZyJMXJnD+3DnatGiGk5MTYZu3ULhwEaPp0Q8e8F6DAJ7Gx7Nr3wG8ixUzaf9S1iN3BU1g44YwNJpkvhg0KEOoADzUaoJCVrNr53ZiY2JksHIBGSwTOHv6NADNW7Z67jw+5cvjU768uUqSLEweY5nA369iVavlKLtSuhwfrPv37rEjfBsJCQmGtt27dnLnzm0LViXldDk+WE7OzvTp1YMKZUsZ2j7/5GOcnZxN3pderzf5Z0rZU44PlouLC40bNzFqa/je++TLn99kfZQpWxaAE8ePPXee06f+ZOSwIZw8cdxk/UpZV44PFkDb9h2M/h3YrsNz5nwz9Rukj62xYumSTKcLIfhjwXyWLVmMjY08X5Qb5Ipg1a5TF3cPDwDy53cjoH59035+3bo0b9mKsHVrWbxwgdEuoUaj4btvRrEqJJgmzZpToWIlk/YtZU255gLxBw3rcfHCBT7+5H+M+XGsyT8/KSmR7l27cPhQJJ6FCuFT3heVSsWVy5e4dfMmHmo1GzZvw0OtNnnfUtaTa/ZL9Lr0rUhg+/aKfH6ePE4sXLKMtatXsWvndk6fOkVMdDQVK1Xmo+6f0qVbNxwd8yjSt5T15JotVosmH3Du7Bmu3LxjththtVotdnZ2ZulLylpyxTHW32xt7cx6d7kMVe6Vq4IlH9mQzCVXBUuSzEUGS5IUIIMlSQrINafbJdN6/OiR4n2oVKrn3np24/p1Fsyby4GIfVjbWNOseUtatm5DseLFFa/rVWQarCePH2d451R2l5aWhhDCLL8QucHbFc3zbFnnrt346RfjIQ3i4uJo37YVZcqWpVfffqhUKqZMmsCcWTMI37WXQl5eZqntRTIEa+SwISxbstgStZiFuX4hcjq/d95VvI8jhyI5f+5shvY5M6eTnJTE3AV/kCePEwB58+bls08+ZtnSxXw9ZJjitb1MhmCdP38OMM8XJ2VfA74cpHgfn3TLfFTj8G3byJffzRAqSH9iwd3dHV2aztC2fOkSfCtUwKe8L+vXrSUmJhoPDzXNW7bCzs6O+/fusT5sHTpdGt7FitOkaTOT1Z7prqC1tbVZvjhJehNFihblyKFI7ty5TZEiRQEIW7eWmJgYChQsaJhv1oxpvFuzNlevXOba1avky5+P69eusW3rFvoN+JLOHduBEKSkpJCSksK0mbNfOLzC65BnBRVw8cJ5enzaPdPdGOm/mzZzFtVrvEND/zp06dSebh92ZGD/vlT3q0Gnzl2M5g0OWk7VatWIPHaCXfsO8FmPnmzZtJGPOneiX/8viDx2go3btlOtup9JD4FksExIp9MxbcpkfhwzmuTkJH76YQxTJ08kLS3N0qXlKElJSRQpUgSVygpNsobY2BhUKhUNGjXCycnJaF61pycjvhmNvb098M+AP/UbNqRH7z7kyeNEqVKlqVq9OqmpqSarUZ5uN6ED+yM4FHkABwdHXPPmJT4+jsOHIqn8dlX8A+pZurwcQavV0rlDe7TaFDZuDadkqVIIIVi3dg1f9uuDNkXLl199bZjf2sra6FY2K6v0bcmzu4xKkFssE7pzO32AmsJFiuLpWciw/3/n9q0XLSa9hv0R+7h08QKdOnehZKn0cUxUKhWt27Sldt26zJwxjadPn1q4Shksk7L66y9jfNwTdDodcXFx6e1W8ms2FRcXFwDs7OwzTKtXvyEpGg0H9keYu6wM5P+4CdWqUxdHR0diYqI5e+YUMdEPcHB0pGbtOpYuLceoWKky9vb2PP3rZRN/E0KwedMGACpUrGiJ0ozIYywTKvrWW/w2eSqbNoRx/Ngx3q5ajWYtWuLq6mrp0nIMe3t7Pu/ZiyWLFuLj68u7NWthbW3N3FkzOX70KB0/7JzpMN/mJoNlYq6urnTq3JVOnbtauhRFvWioN1N53tnU/l8OIjY2lh6fdsfZ2RlbWzseP35E0+YtGDV6jOJ1vYpMg6XT6czyxUnZ18Txv5iln8yOpezt7fl5/AS6f/oZ+yP2kZqqpVbtOlSqXMVovuXBoRnueS1Tthy7Iw7imtd4L6J3336kaFJMVneGMS8+6tyJvXt2m6wDKWca+e13ivehUql47/0PsuXbWTIE68qVy+zeuTPH3d0+f+5sYmNiGTpipKVLyRE+79nL0iVkablqlKYrly9z/so1S5ci5QLydLskKUAGS8rSzp45w6KF8y1dxmvLEKzpU6dw88YNS9SSo0Q/eMCkCeMNL6XL7ubPncPFC+fN3u+cWTMYPWokcU+emL3v/8IoWOfOnmX8z+NYuWK5perJMYJXBjFl4oQccdki6u5dfvjuWxYtXGD2vv++lpWmy15PCBgFKy0t/bb57LYSWVHaX48g5IRHRgy/3GnP3/r+PabI6zLloxpZyRsdY2m1WlPX8cZM9R/zugEwVb/Z+bsUQvDnyRN8O3IEv4wb+0YjDe+P2EdgqxYsX7qE+H/d/5edvXKwYmJimDdnNi2afMDlS5eUrOm1zJ87m/59erFr547XPp7R6/UcijzIkK8GMnvm9Nda9tbNm7Rs2pjZM6YT/eDBay0rhODokcMMH/I134/+5rWWVVJSYiLdu3Zm8oTfuH3r5gvnnT51Co0C6tKqWRMW/7GAJk2bv1Gf775bk4cPYxkxdDB+VSrSt1cPdm4Pz/Zb+hfeK6hJTiZ821ZWh4awZ/cu9Ho9VatXx7dCBXPV91LNmrdg4vhfWb9uLe4eHrRu05bA9h0p5+Pz3GWuX7vG6lUhrAkNNbzke1/k4dfqt2SpUuTNm5dxY3/gl3FjqVPXn7btO9C4cRMcHB0zXebWzZusDg1h9aoQbt1M/8WdMn3ma/WrpLz58uHu4cHkib8xeeJv+NV4h8D2HahcxfhWobt37zD+53FGbW1b/veBWFJSUti4PoyN68MoWLAgrdq0zXAXe3ZhdIH41J8nadm0MS1btyFPnjxsXB+WJR4aexM+5cvTtl0HWrdti7u7B03fb8TlSxepWKkSx48pd0LBycmJps1bIASEBgexYPFSoh88YFVIMEcOH1KsXyXZ2dmj1aZQukwZChR0J/LAfsX7fOfdmgS278CWzZvYuT2cY6fOUKCAsk/9mlKmWywnJyfKlivHmdOnOXP6lLlr+s8cHfNQtpyP8VZLCKysrChbzofLly4p9gfDu1gxypbzMWwJdWlplCpdmrLlynHx4gXi/3r4MTvxUHtw5/ZtChb0oFTpUly6cIHxEyexKjSE8K1bSE1NZXfEwTcahVar1dK4UX2uXb1KseLFCWzXgTbt2hmevt6ze5epV8c8xDP+PHlCeHupxdgfxhjaLl44L8b9+IPwe7uS8PZSiw5tW4usJDkpSfiUKi68vdSiU7u2ImRlkEhISMgwX/PG74tyJYunL5OcLDaErRPdu3URxYsUEt5e6kyXeZnu3boIby+1qF6lovhxzGhx/tw5w7RJv40X3l5qcfDAfkObRqMRmzZuEJ91/0iUKOolvL3U4vChyDdYa+VMGP+L8PZSi0rly4qRw4aIY0ePips3bghvL7UYPGigEEIIrVZrmP/J48di6eJFYtOG9W/U372oKDFi6GBx9MiRTKf36fm58PZSi9jYmDf6fEt56fNYZcqWY9jIUQweNpwD+yPYELaOxMTEDKPhWMrZM2fo0/8L2gQGvvIDbg4ODjRr0ZJmLVoSExND2No1HD92lLr+Aa/cr0ajwcvLiz+WLqeufwDW1tYvXcbe3p4mTZvRpGkzHj6MZf26ta994kNJOp0OG2sbZs6dT8NG7xlenPf38eDfbG1tDT/nzZePLt0+euM+PQsVYuzPv77x8lnVKz/oaG1tTV3/gJf+8l25cpmF8+YaztDZ2zvQs3cfvAoX/m+VPkc1Pz+q+fm98fLu7u787/Mer72cg4PDf/qFKFCgIN0//eyl8129coWF8+cazpLZ2dnTs08fRZ6Stba2ZsBA0w/U+vBhLOfOpo+xWKJkySzxhK/STPoE8eaNG/iyf1+KvuWN2lONXqfn2NEjrA4NZvf+g9nq4DMr2LJ5E1/064O1lRVVqlZFCDh25DCrQ4MJXbv+hWc+s4K0tDQm/fYrC+bNIzk5CQAbGxvadehIn34DeMvb28IVKsdkN+HGxcXRr3dPmrdsRfiuPSwLCmFFyCrCNm0lISGBrZs3m6qrXOHp06f069WDEiVKsOfAIZavDGVFcCgbtmwjMTGRUcOHWrrEl1q0cAErli1j1rz5nLt8leXBobQJbEfQ8mVs3BBm6fIUZbJgHT92FJ1OR0C9+kZX4Mv5+ODlVTjDF6nRaIiOjmb7tq2sXb2Ke1FRFru9Ra/Xs3jhAsZ+/x0N/evw+ScfM/7nnyx64+eJ48dIS0ujZ+++uLu7G9rLlC1Hi1atibp712h+rVZLdHQ0O8K3sWZVqEW/T0j/Tg9HHuTDLl0IqFefPHmcqFW7DmN//hUrKyt2hIe/0ucULlKEAgUK4uTkrHDFpmW0K+jhocbW1hZv79d/FLpe/QbsO3go0zEKdHod96KiDP+O2LuXAX178+jRQ/LndyMpOYkUjYb6DRoyc+58HBwc3mBVXqxwkSKkpma8fSglJYXAVi24dPECvhUq4JrXlevXrhG+bSu7d+1i+coQ8ubL90b92djYUPgNjy39A+qxL/Iwtja2Ru0pKSmGgUH/dub0aUYMHcypP0/i5OSETqdHo0nGP6Aecxb88Z+/z3z585MnTx68i736rpuVlRWz5y80/Fun03H+3FmuXL78WvcUDh46nL79BijyO6Gof58mfPgwVuh0OpOddty7Z7fw9lKL8K1bhBDpp2prv+MnSnkXEZEHD4jU1FQRHR0tRo8aKby91GLKxAkm6/tZyUlJIj4+PkP7/oh9wttLLYYP/drQptfrxbIli4W3l1p8P/qbN+pPp9Mpcop4/769wttLLbp0bG9oa1C3tij5VmGxb88e8fjRIxETEy3GfDtKeHupxeeffGySfh8/eiRSU1Nfa5n4+Hgx5KuBooqvjyhXMv2SSOvmTYS3l1oEtmphkrqyqgzBMqWjR46I8qVLiBZNPhB6vV4IIcTly5dEp/aB4scxozPMX+ddP1GzelUlS8ogOSlJrA4NEWdOnzZqv3D+nPD2UotvRgw3az0vcvzYUeFbpqSoUbWyuH7tmqH9y/59xQ/ffZth/oDa74oaVSubs0QDrVYralStLHzLlBQ/j/1RrFuzWty5c1sIIUTJtwrn+GApMq6gEILgoOV8O3IEBQoUZNrM2YbjrlKlSrMiOBRIPzV/+9YtDkdG8vBhLA9jY8mXL/N3zirFwdGRlq3bcPhQJKOGD0Wr1ZKcnJzlRqoKDlrBNyOH4+bmxorgVUZ3OUz6fRoA0dHR3Ll9mz27d3IvKorYmBicnC1zbHLm9Cke3L/P0BEj6d23v6E9NTUVvV5vkZrMyeTB0uv1jB41giWL/qB+g4ZMmPI7bm4FjObZs3sXs2ZM5+BfY2yX9/XFq3Bh9Hrzj2uj0+kY8tVAVoUEU+Odd/EuVgz/gHrUqevP0K8t//I9IQSjR41k8R8LCKhXn4m/T81w2eL0qVP8Mm4skQf2k5aWhtrTk/K+FdDpLPcL/OCvC9/PHg9qtVqmTpkkg/W6hBCMGj6U5UuXUL9BQ+YvWpLhhQCPHj2kx6fdKVGyJDPnzqdadT88PDwAqFuzhtGrLs3hl3FjWRUSzLKgEGrVqWPYsip5o+6rEkLw7cjhLFn0B/4B9Vi4ZFmG7/Pxo0cMHvQFQsDv02dStVp11J6eqFQq6tWpSXJyskVqf/+DxviUL09w0Aq0Wi353dw4evgQt2/doryvLw8e3CcpKdHodac5iUmDNWnCeJYvXYJfjXf46Zfxmb5lY9uWLaSkpNCzTz+jd77evnWTu3fu4OlZyJQlvdTVK1cAqFSliiFUOp2OmdN+N2sdmfl90kSWLPqD6n41GDf+t0y/z/BtW7lw/jwTp0ylafMWhvZLFy9y+9YtCj5zqt6crKysCNu0lYMH9rMhLIzjR4/SrEUrunTtxvXr17l+7Sqp2lTIY5HyFGeyYJ08cZzZM6bj5VWYr4cO486d24Y7vAHs7OyoXOVtw/1nRw5F0qBhI1xdXbkXFcX/un9skV2EqtWqsSN8G6OGDaHrx91J0aQwf+5sTpw4bvZanhUbG8PM6dPwLFSIwcOGE3X3rtG1K8P3+debCo8dPUKbwHaoVCru37tHn56fWXwgG1tbW/wD6mV46Z5P+fL4lC9voarMw2TB2rd3DykpKURF3aVjYJsM04sUfYuIyMO0bN2GPbt2smzJYg5FRmJvb0fU3Sg+7NIVIQSxMTFoNBqzXbfo028AiQmJzJj2O+vWrsHdw4Peffszc848PuryIVeuWOZp6R3h4Wg0ydy/l5zp9+nlVZgDR47RomUrdu/cwbIlizl86BB2drZE3Y2iU+cuVKxUmZ07tqNJTn7uw5eSMkw2Em58fDz6F/yFVFlZkTdvXiD9HrKF8+fx9Gk8zs4utO/QkfxubmiSk9FoNORxcjJs2cxBCGG4y+LZvp8+fYouLY28+fK90XgO/4VGo0HzguOjZ79PnU7HwvnziI+Pw9nJmXYdO+LmVsDwGeb+PqVcNMS0JJmTHAlXkhQggyVJCpBvdJRM6kDEPubNnYP46wyvb4UK9PtiYPa7ifY/klss6ZXo9fqXjt2+IWwdnTu2J1Wrxa1AAVxcXJg+9Xc+6dYlV9xtYcRSNylK2cvePbvF1wO/eO70pKREUcXXR/z0w/dG7WFr14hihT1FyMogpUvMUuQWS3olq0KC2bRh/XMvAZw4doy4uCe8Xa2aUXuLVq1x9/BgVWgICQkJnD71Jw/u38/0M86eOcOjRw9NXrslyGBJL5WYmMjWzZtJTExky5bMh1ioVacup85fomat2kbtKSkppKSkkPD0KUIIOrRtw1dfDsiw/OXLl2j2QSNiY2IUWQdzk8GSXmrzxg2GwWBWhwQ/dz5nZ2fDRWtIPy7r16sHcU+eMObHn3BxcaFNYCAR+/Ya3e4GELIyCN8KFShTtpwyK2FmMljSS60KDTH8HLFv7yuPhbh08SLCt22lfsNGVP1rF7FLt48BCF250jBfamoqq0OCaRPY3oRVW5YMlvRCUXfvGo3VrtfrWbMq9KXLbdm8iTHfjuKzHj2ZOXuuod23QgXerlqVkJVBhjOFO3ds5+HDh7Rs1dr0K2AhMljSC23dsslokFb/gHqErVtj2DXMzJpVofTt+TlDh49k1OgxGW4A7tLtY+7evcPB/emBDQ5aQV3/ADzUamVWwhIsfVpSytrS0tKEEEJ4e6mFt5daCCHEzRs3Mp1Xo9GIfr17Cm8vtZg9Y/pzPzM5KUlU9Ckjen3+P3Hnzm1RvEghsWZVqOmLtyB554X0QpmNSZ/ZCLZarZbePT5j5/Zwho4YSY/efZ77mQ6OjrTv0JH5c+fg4OCAvb0D7zdubNK6LU0GSzKJX8eNZef2cHwrVKRIkaKsX7fWaLqTszMNGjYy/Ltz14+YP3cOa1evok1guxz3iL58bER6JcUKewJw427mF3f9a72T4a0kzypRsiQ79xq/sO7DDu04uD+CpSuCqePvb7piswC5xZJM4qshw0h4wcv8XF1dM7R9M3oMJ08cp2bt2pkskb3JLZb0Sl62xZKMydPtkqQAGSxJUoAMliQpQAZLkhQggyVJCpDBkiQFyGBJkgJksCRJATJYkqQAGSxJUoAMliQpQAZLkhQggyVJCpDBkiQFyGBJkgLkg46SSa1YthQHBweaNG3GtKlTiI+Lx7OQJz169cHGxoZtW7cQsXcvAA0aNaJe/QYWrlgZ8kFH6ZW86oOOPT7tTlRUFNHRD1CrPbGysuLPkyfwq/EOder6E7IyCO/ixbh+9RrR0Q/YsCWccj4+5lgFs5K7gtJLXbly2fDziKGDiY6OJmRl0HPnP3P6FHXqBrBu42bWbthEzdp1OHrkMNN+n8ysefNZFhRC2OYt5M+fnwXz5phjFcxOBkt6Lp1Ox89jf+T9+v8M2Ll86RLq16nJ4EFfsmvnjkyXK1O2HD/+NA4rKytUKhX+AQEIIfh+7DgqVKwEQMGC7nioPdm1Y7tZ1sXcZLCk55o88TdmzZiGja0tRd/ypkxZH7wKF0Gj0aBSqRgxdHCmL5SrVLkyeZz+Gc5MpVIBUMjLK8O8Go1GuRWwIBksKVO3b99ixtTfsbOzo3TpsuTP74aDgwMFC7pTomRp8ud3415UFIcPRVq61CxJBkvK1Mb1Yeh0OjzUnhlGw3V0dMTW1haA+Ph4S5SX5clgSZmKj0sPjK2NbebTn6ZPr+7nZ7aashMZLClT1WvUAP4J0L8lJyXxQeMmuLkVMGdZ2YYMlpSpWrXrULToWzx6GEt8fJyhXQjBgwf3cXNz44effrZghVmbvEAsPdfBA/vp2qkjOl0azs4uODo6kpCQQHJyEkdOnsbd3T3DMqmpqQCGYzCAtLQ0dDodtra2WFn987dcq9UihMDe3l75lTEzucWSnqtmrdqs37yVt6tWIyHhKTEx0Wg0yTRp1jzTUEF6oJ4NFYCNjQ329vZGoQKws7PLkaECucWSXlFsbAxnz5zBp7wvHh4eli4ny5PBkiQFyF1BSVKADJYkKUAGS5IUIIMlSQqQwZIkBchgSZICZLAkSQEyWJKkABksSVKADJYkKUAGS5IUIIMlSQqQwZIkBchgSZICZLAkSQEyWJKkABksSVKADJYkKUAGS5IUIIMlSQqQwZIkBfwfRGQd3Lz2MzkAAAAASUVORK5CYII=)
physics-General
physics-
A uniform triangular plate ABC of moment of mass m and inertia I (about an axis passing through A and perpendicular to plane of the plate) can rotate freely in the vertical plane about point 'A' as shown in figure. The plate is released from the position shown in the figure. Line AB is horizontal. The acceleration of centre of mass just after the release of plate is :
![](data:image/png;base64,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)
A uniform triangular plate ABC of moment of mass m and inertia I (about an axis passing through A and perpendicular to plane of the plate) can rotate freely in the vertical plane about point 'A' as shown in figure. The plate is released from the position shown in the figure. Line AB is horizontal. The acceleration of centre of mass just after the release of plate is :
![](data:image/png;base64,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)
physics-General
physics-
Two identical uniform solid spherical balls A & B of mass m each are placed on a fixed wedge as shown in figure. Ball B is kept at rest and it is released just before two balls collides. Ball A rolls down without slipping on inclined plane & collide elastically with ball B. The kinetic energy of ball A just after the collision with ball B is :
![](data:image/png;base64,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)
Two identical uniform solid spherical balls A & B of mass m each are placed on a fixed wedge as shown in figure. Ball B is kept at rest and it is released just before two balls collides. Ball A rolls down without slipping on inclined plane & collide elastically with ball B. The kinetic energy of ball A just after the collision with ball B is :
![](data:image/png;base64,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)
physics-General
physics-
A child with mass m is standing at the edge of a playground merry-go-round (A large uniform disc which rotates in horizontal plane about a fixed vertical axis in parks) with moment of inertia I, radius R, and initial angular velocity
as shown in figure. The child jumps off the edge of the merry-go-round with a velocity v with respect to the ground in direction tangent to periphery of the disc as shown. The new angular velocity of the merry-go-round is:
![](data:image/png;base64,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)
A child with mass m is standing at the edge of a playground merry-go-round (A large uniform disc which rotates in horizontal plane about a fixed vertical axis in parks) with moment of inertia I, radius R, and initial angular velocity
as shown in figure. The child jumps off the edge of the merry-go-round with a velocity v with respect to the ground in direction tangent to periphery of the disc as shown. The new angular velocity of the merry-go-round is:
![](data:image/png;base64,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)
physics-General