Physics-
General
Easy
Question
A piece of wire is bent in the shape of a parabola
-axis vertical) with a bead of mass
on it. The bead can side on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the
-axis with a constant acceleration
. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the
-axis is
![](data:image/png;base64,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)
The correct answer is: ![a divided by 2 g k](data:image/png;base64,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)
Related Questions to study
physics-
A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out length
where
is in metre and t is in second. The radius of the path is 20 m. The acceleration of P when t =2s is nearly
![](data:image/png;base64,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)
A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out length
where
is in metre and t is in second. The radius of the path is 20 m. The acceleration of P when t =2s is nearly
![](data:image/png;base64,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)
physics-General
maths-
The equation of the plane containing the line
where al + bm + cn is equal to
The equation of the plane containing the line
where al + bm + cn is equal to
maths-General
physics-
A small body of mass
slides down from the top of a hemisphere of radius
. The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is
![](data:image/png;base64,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)
A small body of mass
slides down from the top of a hemisphere of radius
. The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is
![](data:image/png;base64,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)
physics-General
physics-
Average torque on a projectile of mass
, initial speed
and angles of projection
, between initial and final position
and
as shown in figure about the point of projection is
![](data:image/png;base64,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)
Average torque on a projectile of mass
, initial speed
and angles of projection
, between initial and final position
and
as shown in figure about the point of projection is
![](data:image/png;base64,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)
physics-General
physics-
A string of length
is fixed at one end and the string makes
rev/s around the vertical axis through, the fixed and as shown in the figure, then tension in the string is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAL4AAADPCAMAAAB81JvLAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAALoUExURf////39/f7+/sDAwE5OTiwsLG9vb9PT09HR0d/f38nJyTc3N01NTbe3t7a2tlJSUmlpafT09JSUlAAAAI+Pj3Z2dnR0dL6+vhsbG0xMTOPj4+jo6OLi4vf394aGhhAQEGdnZ+fn5+zs7FxcXAEBAfv7+9LS0vj4+Nzc3DY2NhkZGZWVlZ6enpubm3JycnV1dTs7O7q6un19fQkJCZqamn9/f1dXV3t7e3l5eTU1NXx8fOvr68/Pz+np6V1dXZmZmczMzM7OzsvLy9DQ0M3NzdjY2Pb29tra2mJiYlFRUVZWViAgIEtLS1RUVEhISHh4eOHh4cXFxcfHx8jIyEpKShISEpKSksTExNbW1vn5+WtrawcHB/r6+mNjY7y8vHBwcJeXl25ubn5+fvX19b29vXd3d7u7u+Dg4I6Ojq2trY2NjVpaWvz8/HNzc7i4uL+/v66urllZWVhYWF9fX4ODg2RkZMLCwrKysmxsbK+vr2FhYcbGxrW1terq6vHx8fPz84CAgGpqalVVVV5eXsrKyrCwsKioqIGBgYKCgqurq9XV1VBQUIuLi+bm5p+fn1tbW9nZ2ZycnKOjo7m5uaqqqiYmJu/v76SkpD8/P0VFRUdHR0lJSdfX14eHh97e3kJCQuTk5IqKitTU1EBAQPDw8ENDQwYGBi0tLXFxcfLy8oiIiHp6ekRERJ2dnYyMjC8vL0ZGRuXl5Tw8PO7u7qGhoWhoaJGRkSoqKpaWlhoaGqCgoFNTU4SEhG1tbWVlZcHBwWBgYKmpqe3t7bGxsbS0tKampqWlpaysrMPDw5OTk09PT5CQkGZmZoWFhaKiorOzs4mJiaenp93d3RgYGD09PSkpKRcXFx4eHhUVFRYWFhwcHC4uLjAwMAgICDk5OT4+PhMTEzQ0NDg4OCcnJwsLCyMjIxQUFCQkJNvb2yIiIgwMDB8fHyUlJSEhITIyMkFBQQ4ODjExMTo6Oh0dHSsrKzMzMw8PDwAAAFcKgFsAAAD4dFJOU/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////8AKM62NwAAAAlwSFlzAAAXEQAAFxEByibzPwAACN5JREFUeF7tndGV4yoMhtODC3Ap0AwUQg1UweFNbfBEFy6A9wVMMrETI8fBBs7m23N3krlnZskfISQhyO3Hjx/H4GIy1Nr0rDeo05wLk551BxnI7ca6HT4fNdygV9u53dQoID3sERCDSg+7g1I/fjfy9LQ3CPGGQ4ZeZy5zXngVnE+XMMGYcSw96w4K1Ihetf/x40ej0BLYWjGRFRr5I8YpPsj9xarFo0m/baweSXq4TfplLWK6jRgiRpte482AIazbkMcDN961/P4NQORvPJdE5LdKpkcNQr22iPxKpAcNwnyejshPTbvyi6C8ySe7DcsvQpWkX/mj+liVsF35SRSWi2xg0678EL06qLz8pGHnE8DkF22vzIBYf6vyyySrFNmkxOo25Y+O0wP5wBMalX92nJ4+5X+UCCGEDxnalF/ou8shU1bfNuUnwigpOZeETTp97z1tyg9SOCGE00TlN7ladT5+ZLEUhVq/aS/vmoOGGe6y4wPXXsXnORNE5AfFmpP/vmxFuM77/lf5IZKeVGAxfIvJr9YjpYoxUnFP/rHqRmje+l/lp2aYag7fpFV3tgDLshVPPznWL4+MVedzMlyu54CfOyTyWQ9WufSgJlzIOZ+F+7uxwVp+uzS+SvhkJU3bD50P13Wz4FBlu/GQipMY8mDym6X8alpPhmuJmsdwIOmOyb+0flHZ9OcqW7B7OteqPpKf62hx9RauuGzFPP3uND+Rn0zhiVXZnziToD6IiTFj0gIMSGD8J79V0+hzBVWxETFU2UA4pRQz8/D3Z73UGMPCD9ZLBKLZGnODG72vuLvlBxuo38PKwtS1j0ImIn9zJbe44v5N2f3WX51YZYv1fakfgyLdyB/dDfhZ+1xm60f+OeSSIWR7UpyYTuSfnT0QsdiBACQSa0b+u7Nf9Y30Iv+9QL4Clb+FMD8DIn8MsRumE/k3Y12S7wGTZjlZKrHZb4HJvygQVWM71VZ5629D/m0RQWTlDyt1fTKFDkR+0oL8mcwW8q3xTcify7JVF85nE9uD9Wdg+f0IJCu7glhl2wKJzBqQP78hwfK7cfXlzzhOT6q8bQHVIx9kAK3Ln1cfa9JD+lDOhyBpE9KmVFt+rDiM5CXIXmR9MPnz9ejqoNZfVf6NVP0JpAe1rvx40sSRpbeq/IjjDKDyI7P/THakrC1HPjv+bawJkleUH5+6wfqzeYlF9iKr07D8e0DkB1lt+Pt2lJs9f7DvVBN9aYRpAS/9Dr/vwY4nXAmE/Vj/1RImpFb+K5Hhec6O2pidsesPtBtDzxp348icuslpHIO4lMnNxL16XuKHQJUIdT8btvLjN/yLCT7bchlMW47+5cRvh/+5AmnUOJkwJGtGx8I4n8f3dBAdgMZFjAn2+i7UlB9kqJcBzRZ17gDR45v2QFpNfq7HaZd/TIAN65BdvtgYGEP8czGSRc/ylu12EOLcos2IOqKEMCLzy0pDWez8ywi2HW55I3q+9smawSniUcbpS6IEINOIFTJyy5bl/ofneW6NJmRuggTvqEQ+CCoEMRy74gJNV7hmcKNG8dnJzlhy9q0+Ydg73mI0aPDuVjMT7rDy1v/3VvJTg3xQO9tbsSqb/1XS3f3W/Cpm6Inj965yp5t+u8QusQ9DWfTHn9gXQJc+7yuAhIBozlie5cfaHr4ACjqGuc7DR+fFXkQ+9pQSA/3IKXPU9lOoz12YuOJZ/jPKyxI5/LZibkLO8DjoTcPIF5HPCSUGPoU3eT/o9s6qq3Ahf/kUWH24HqLLVmxRvcMlf341pPxdmB/+QnT6Ler7ZGT6qQtPlo0ddjjxNTHPyrDaPGSDeNqq5kXbAnjMpcqyrn+z538D2br4DOvyB4aPkbu/pGhThhkPrOKovS2m7oqSjv/YIohW2V6do32kW/Vrh2jA/GrfZEyrFXY3xQWgfv915xZcPHBTdObSg1aI1zhf1yY+za+oXOET9MEFEA9b3mwdzloVDPgf9vgpO1a6jbW1YN0NdP6g6ne8vyJAFbw4gJ2wYP2xOFkRkZKVzLUOC7FrygNZ2w8bT8sUP+J1Xr5lWZgC5YZihv8V+zaH/LukhFacAlhKhGPcFdxu+eIkzI6mgBmghAmhtRax4kb9f4WwX7yTe9UPAOfhMpnSRi+/uEB/T1PAyZAvdl2Pm0A549m16VOY1vvHEdRUvMhzgMO2z6dSnv8b29FHB2F1IfUpcjw1y26//8LRDGONHKoMvxTymztmavbRzXyzaqFVtk2g1AUB/Eh952v+toy+hFYZPp0KJepwbqq1QTm/XwVeyu9XotxHUlSI2AoC9e7HKQH/qNmoDLbgx5lMJ2ywIpDPNjCzmJfL9k5HF/wnP9tIL4Ht2+sjhxmb58AebAaoka2XQ4aP7LuM4lL5+O9C+cvfccAu/OgjG1t7imLVZa4fDu1/t8Prla5dUdZp3rnQfs6ATlccMDmvok4u2C+T43mFIXN24Ax8b3fuEUrmEO+ZzwOcyDlu4c7pnwEuz/tUx9MnlpeHDeYcEwJyyfX7ajylRcuq4ZqDf/yM4A28V04PLwCKG5C9sibIXcHsvVgpfzd29+kPHKviScxLgXTK6nu4q9K7E9evAouYZdWSE7U4LfApEHe+zl3Gs0g3HG/LtkRfb/QLAGIMcUw/7lzNzyRJ+LFz8WFND8K47bt983BM/+pL06kZU9/uHoDoaXOr2Ipp0sJde5Ex0OA+gGfuAohYHryt0mZ70ePjoCiZri/Jhx6cMbRvAKcru5hLpNxN81UB2YjDhQ/7EDU+ENxyGaoRoKcp1MlAMRa2xahxU1iZqGYEFdVOIW42Ffs4gah4WZ81On5kPQ0H0IPgy7fkPSpMC3Df9FGUgnojinYS/9pH2BWiYuqk0AZW8hkZGzjt6JjQ+WtSW4IIk4itE2RgZEiHPyC9MM8es6sB0DRATxijnuzNpOHL9Lo8nbwbdvRznqdQyMbPl/SvS/JO9qZU6JuDS4qpJ2DdEOzGDD12UYD0sVNYKPgUv/RGWKXDiVEfhne+Lf3jx4//l9vtH6TuxEWbVlO5AAAAAElFTkSuQmCC)
A string of length
is fixed at one end and the string makes
rev/s around the vertical axis through, the fixed and as shown in the figure, then tension in the string is
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physics-General
physics-
A thin prism
with angle
and made from glass of refractive index 1.54 is combined with another thin prism
of refractive index 1.72 to produce dispersion without deviation. The angle of prism
will be
A thin prism
with angle
and made from glass of refractive index 1.54 is combined with another thin prism
of refractive index 1.72 to produce dispersion without deviation. The angle of prism
will be
physics-General
physics-
A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if
. The index of refraction of glass is
![](data:image/png;base64,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)
A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if
. The index of refraction of glass is
![](data:image/png;base64,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)
physics-General
physics-
Which of the following diagrams, shows correctly the dispersion of white light by a prism
Which of the following diagrams, shows correctly the dispersion of white light by a prism
physics-General
physics-
A ray of light incident normally on an isosceles right angled prism travels as shown in the figure. The least value of the refractive index of the prism must be
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)
A ray of light incident normally on an isosceles right angled prism travels as shown in the figure. The least value of the refractive index of the prism must be
![](data:image/png;base64,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)
physics-General
physics-
A ray of monochromatic light is incident on one refracting face of a prism of angle
. It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the material of the prism is
, the angle of incidence on the first face of the prism is
![](data:image/png;base64,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)
A ray of monochromatic light is incident on one refracting face of a prism of angle
. It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the material of the prism is
, the angle of incidence on the first face of the prism is
![](data:image/png;base64,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)
physics-General
physics-
A light ray is incident upon a prism in minimum deviation position and suffers a deviation of 34°. If the shaded half of the prism is knocked off, the ray will
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)
A light ray is incident upon a prism in minimum deviation position and suffers a deviation of 34°. If the shaded half of the prism is knocked off, the ray will
![](data:image/png;base64,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)
physics-General
physics-
A prism ABC of angle 30° has its face AC silvered. A ray of light incident at an angle of 45° at the face AB retraces its path after refraction at face AB and reflection at face AC. The refractive index of the material of the prism is
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)
A prism ABC of angle 30° has its face AC silvered. A ray of light incident at an angle of 45° at the face AB retraces its path after refraction at face AB and reflection at face AC. The refractive index of the material of the prism is
![](data:image/png;base64,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)
physics-General
physics-
A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the angle of emergence and each of these angles is equal to 3/4 of the angle of the prism. The angle of deviation is
A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the angle of emergence and each of these angles is equal to 3/4 of the angle of the prism. The angle of deviation is
physics-General
physics-
A small particle of mass
is projected at an angle
with the
-axis with an initial velocity
in the
-
plane as shown in the figure.
the angular momentum of the particle is
![](data:image/png;base64,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)
A small particle of mass
is projected at an angle
with the
-axis with an initial velocity
in the
-
plane as shown in the figure.
the angular momentum of the particle is
![](data:image/png;base64,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)
physics-General
physics-
The figures represent three cases of a ray passing through a prism of angle A. The case corresponding to minimum deviation is
![](data:image/png;base64,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)
The figures represent three cases of a ray passing through a prism of angle A. The case corresponding to minimum deviation is
![](data:image/png;base64,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)
physics-General