Maths-
General
Easy
Question
If line 2x + y + λ = 0 is normal to y2 = 8x than λ =
- 24
- – 24
- – 8
- None
The correct answer is: – 24
To find the value of λ.
![y squared equals 4 a x
2 y fraction numerator d y over denominator d x end fraction equals 8
fraction numerator d y over denominator d x end fraction equals 4 over y
s l o p e space o f n o r m a l space o f space p a r a b o l a equals fraction numerator negative y over denominator 4 end fraction
G i v e n comma space 2 x plus y plus lambda equals 0 space i s space a space e q u a t i o n space o f space n o r m a l space o f space t h e space p a r a b o l a space y space space 2 space space equals 8 x.
S l o p e space o f space n o r m a l space equals negative 2 equals fraction numerator negative y over denominator 4 end fraction
y equals 8
f r o m space p a r a b o l i c space e q u a t i o n comma space x equals 8
p u t t i n g space t h e space v a l u e s space o f space space x space a n d space y space i n space t h e space e q u a t i o n space o f space n o r m a l space 2 left parenthesis 8 right parenthesis plus 8 plus lambda equals 0 space rightwards double arrow lambda equals negative 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)
Therefore, the value of λ is -24.
Related Questions to study
physics-
A disc of mass 2 M and radius R is placed on a fixed plank (rough) of length L. The coefficient of friction between the plank and disc is
= 0.5. String (light) is connected to centre of disc and passing over a smooth light pulley and connected to a block of mass M as shown in the figure. Now the disc is given an angular velocity
in clockwise direction and is gently placed on the plank. Consider this instant as t=0. Based on above information, answer the following questions: Time
up to which the block remains stationary is
![](data:image/png;base64,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)
A disc of mass 2 M and radius R is placed on a fixed plank (rough) of length L. The coefficient of friction between the plank and disc is
= 0.5. String (light) is connected to centre of disc and passing over a smooth light pulley and connected to a block of mass M as shown in the figure. Now the disc is given an angular velocity
in clockwise direction and is gently placed on the plank. Consider this instant as t=0. Based on above information, answer the following questions: Time
up to which the block remains stationary is
![](data:image/png;base64,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)
physics-General
physics-
A disc of mass 2 M and radius R is placed on a fixed plank (rough) of length L. The coefficient of friction between the plank and disc is
= 0.5. String (light) is connected to centre of disc and passing over a smooth light pulley and connected to a block of mass M as shown in the figure. Now the disc is given an angular velocity
in clockwise direction and is gently placed on the plank. Consider this instant as t=0. Based on above information, answer the following questions: Time
1 at which the disc will cross the other end of the plank is-
![](data:image/png;base64,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)
A disc of mass 2 M and radius R is placed on a fixed plank (rough) of length L. The coefficient of friction between the plank and disc is
= 0.5. String (light) is connected to centre of disc and passing over a smooth light pulley and connected to a block of mass M as shown in the figure. Now the disc is given an angular velocity
in clockwise direction and is gently placed on the plank. Consider this instant as t=0. Based on above information, answer the following questions: Time
1 at which the disc will cross the other end of the plank is-
![](data:image/png;base64,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)
physics-General
physics-
A hollow sphere is released from the top of a wedge, friction is sufficient for pure rolling of sphere on the wedge. There is no friction between the wedge and the ground. Radius of sphere is R. At the instant it leaves the wedge horizontally. Velocity of centre of mass of sphere w.r.t. ground is-
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)
A hollow sphere is released from the top of a wedge, friction is sufficient for pure rolling of sphere on the wedge. There is no friction between the wedge and the ground. Radius of sphere is R. At the instant it leaves the wedge horizontally. Velocity of centre of mass of sphere w.r.t. ground is-
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gwcRL1dfWsWPExSoWCIxkZCCEYGhZOZGQkwcEhaHW6Hy9MYsCQLMU1ZP2a1bzy8ovs2rsfgNjo4Tz55FMsueuuAZZM4oeQlOIaUlNdxZ7du9m+fRvHjx1Ho1Gj99ATFh5OVFQU8aPHEBEphSYbbEhKcb0Qgn/87a+88Pw/ae00APDS8//kwZ//HDd3jwEWTuJ8JKW4jpzMyyU7K4vs7GxO5eXR2taKWqXG28eHqdOmMWPmLHTOzgMt5n88klIMEFmZJ3jsd79lR+puACaMHcNrr7/BmLFjB1gyCUkpBpDTp05SVFjI2bNnyc8/TW52Do1NjajVaiZMnMjsOXMZN37CQIv5H4c0JTuAhIVHEBYeAUDyurVs2bSZw8ctu6PX1dXi7u6OXq8ndGjYQIr5H4dkKQYRrS3NVFRUcOrkSetLh9vZt3cfHcZu5s6awZ133cXCRYtx95AG5tcSyVIMIpy0OsK0OsLCI9DY2ZGbm4PJZNmgLSc7m7Q9e1AqVUycOImAwEBU6sEV089kMmI2C4wGA0qlEo3djfnZgGQpBjvCTGFBAdu3bWPb1q18s2YtAF4ebsybP58Hlj44KD6PFcJMXm6eZXx0+jSxcbE37HjoJrIUZkBg6uzGaDRjr1UDgubGFsyocHRxxPJangBjO80tBmR2jqgc1Azq/kwmZ8jQMMa3t9Pd3U1FRQWFhQU4OztTXVXF/vR0qioriYyMwtvHG3t7BxwHYPcUc3c327ZuoaiokICAQNra2gBBQX4BWVmZDB8+gqFhN8jYqD/2ybFTysXVFkW/7fvUKYQwierCEpGdniuEaBdCtIiM9D1i775jou68nOa6ArFn82aRnnFSlLb1w6UHgKwTx8VLz/9ThA8Jtu1TNWJYhFjx0YfCZDBcd3nqaqpFVESY8PP2FKu+XCl2paaIzZs2igljEwQgHn3kl9ddpqvlqixFcVERxcVFREdHU1lRgUIhB5OZg+n7iIyKYvfu3fj6+RE3Kr4f1fdHMNVCVznHUveRvCWT0Mnj0Xrp0IkmzIZujhw7gVqtwdtViVzWQbfZQHV+AVvWbGLkrLnETorAUw43Soyj8IgImpqbMRgNHMk4THFxMZ6enmRlZfLav17Fzc0dD70eLy9PPPSe6PX6fn8RsbSkhKqqSjRqNY2NjSxcuAhHR0ciIiPRaXV0dnYwKj6efQcO4uXl1a/XvqZcjSb965WXhYers3BxchB6F52wV8qEnQLh76UXTnYqAYjbFt0iGhvrf7Qs+stSNB0W7YdfEA/Ga609Z6jQJ9wp3nrvKfHBK0uFztqboh0pZt39M/H1+tfFPTNGCkBMWPyEeP6QWZxu77sYA8m3X68SC+cn2SwHIOJjY8Tzz/5DZBw80O/X27Jpo3j0l78Qv/vNo2L5sncvmqeqslKs+PgjsXtXqqivqxNGo7Hf5ehvrspSjJ8wgQceWMqH779HTWMzXq461BoNpZU1KIBAX29GjxmDs7NrP6nuZaBzw37UWAK9PbCnBa+EacTffgcLlvhhV7qfZbKPyBNKPBPvYNyC8SxZMBzjoXT27DiOuauDsmoDneEauPTn5IOe0WMScHRyYvKURE7m5WE2m1EqFZSUlPDRhx/y/nvvodfrCQkJwdvXB09PL/z8/PH28bmq6737ztusXpfM43/8X8aNG3fRPJ5eXkydNo2qqiqysjKJjIzCQ6/vSzWvOVelFGPHjSdsaBhHDmewc3cayGS2mafAAF8eWPoQU6dNv+zy+mcTHDfAl5Ej4xi7sYih825h3N2zCXQBXByYFKXAUx6H/ralJP3EssXnrAkj2OQBzc52NDW0YzAM7mhMP0ZgUBCBQUHMmZsEQGdnB1u3bOGbr1exbs0amto6bHljo4czZ+4cpk2fiV6vR6G88kdh/bpkwLJVanTMpXdpDwgMorSkhJSdO/D187s5lQLAzcOD+NGj2bs3zbIhmnWLGz8/fxYuWsSIH2ikc1gUyVXXH7MlGkCNu4sOpQCFXMm5ECyBONspkXcYkak0aK1fzXr4++CoAoNGhcbegeibbE3Mzs6ehYtuZeGiW6mqqKC0tIS6ujqam5tpbWmhpbWVTRs38Mbrr1lWzkOHovf0xM3NDTd3dzw8PNB7euLr63fR8g8fO8qRw4d54MGHLimD2WymubmJVau+YsXHHzF16jRCQ4deqyr3C32akk0YN54FhYWk7NhOfUs7Hi5a4kaNIvayB9iW9Q2Vqj9mhi29fG1zB0YVdBkN51WuAaPaCWG2Ry0XGKyp7Y0dmDSg1Dhgp1JiBG7Wr6m9fHzwOs9NKirIZ9VXX5F54gTp+/bSYbTYa19Pd+LjRzM0PAx//wCGRUYil8nwtm6gfT4xI2OJGRn7g9dtbGykIP80R48cpqGlnfb29v6t2DWgT0/jrbcuxs3VlW/XrAPgllsWkjht2hWXU1XXyM/uuZu6ujqOHD3Chx99wtx58/n261X89je/pqO9ndi4UaTs3mO5zrwk9qbtQa1R8+xzL/DQL35B+r7t/Prh+6g+WUmrCURlDbUrM9iQ9wGykj0cSq/D5NdG4/EsnjhShvvZVVSdSCO7GFwKKtHt2sXMD77BpTUTuUKNTKFCqVRSX1/PqZMnef7Fl/jZ0gdJ2bmDpfffR1NTEyFDhnDk2HGQyXnogZ+xZvV3yOVyHn7kEZ795wsU5J8mafYsamtrcffwYOPmLYSFR/DUk0/w/nvLGR4VhZNWi8lkQiaToVKpKCstpbyigk8+/YwZM2fx6Scf88f/+W/CI8Jxc3O3xRZUqVTU1tSQX1DAq/96jbvvuZdtW7ew9P778A8IwNvb27b3lkqlQqVUYmdnh9FkoqO9nZycHE6fOsXby5axI3U3D95/Lx99+jlGg4GiokJKSs6gVmvQaNS2jRfs7O1xcHCgo6MdQ5cBVzc3HB0cOH06n7DwcN546+3vzXC5ubnhljCWP/7pceK2biU4JKQvj9z1oT9G6z56dwGIZe+8JUrOFF/Rud4erhfMlgDixX8+J4QQ4g+/++0F6T2cn7Z44QIhhBDvLVt2Yfr/fCh+/q+0C9K0/iPFI/8+JKLn/uGC9Ck/fUbc/fftAhy/J0vP7yd3LBFCCPHOW29ekN7V2fE9mcKGBAshLPE7zk/fn75XCCHE8IiwS16n5/f2m28IIYS49+67fjTvgz+7TwghxL9fe/VH8/b+HTtyWAghxFv/fl0Awk6B0Ltohb3i4vljR0ReNF0JIjVlxwX3tra6WtRUV4n6uhpxtqxUnMrLEx3tg3+Kr1/2pFn64EM89LP7mTMniYDAoCs692Lb4gjroP1K9qEV5gvzvvyHxbz32ETOD+vn7Wjknd+O5l9P3HNB3j/ck8gXf55BdHT4pcu3ytL7OrKLBKi35en96or10GQy/VBVAIsvDtB9GcEpu7utsl3FqzJHjx4BYP/+dAA6u6GmsYWOi1z2rtsXczQzh0d+8f0xhAl45OGHmTB2DH7eerT2Gjw9PdF7euHmrmfnju2ERURg9wO7RQ4W+uU1j1tvu43Ojg6Cgq98T9XqmjoAkmZNJz+/gNNFZwgdahmIjYw956+GBgfa/o6LGcHRE1mAZRoSICDo3P/dXbQM8XUB4CdLFvHlN6sBuGWOxbWbPi4KR42Sti4TKpnlGODO2+aTmXmU0OAAtE5OyGQy6urqKSmvJMH68c/5dXTTOdmUOmn2TDZt3W4pf8ZMABwcHVHJwChAATg6WiYUpk6fzsmCDxgaHIiTk6NNARQKBeXl5VTVNdrcjNFjEli56hsCfb1xd3ezKYlCoaCuro6S8ioSxlraICRkCABe7i74+vpeUqEUCgUlJaXUNbXg7W0ZZ0QMs3wrHuDjhZub6wUy1dXVUVpRTdL8BQDMnjuXd9/7AF9Pd/R6T5pbmpEhw8fbm/b2DpqamkBA+NAh5OUXAlBeXn5RWQYl/WFuTEajMFzlqwWAcNc59YcYEoOEs2Vltr/fX/aOAMRzf//bAEp0ZfTNUggBMhkKpRLF1RUAgEz+n7ez4M2Mr9+5KVwfX8uslcFguFT2QUffnsaL+NNXWAAADY03TmB6iR9HnDe2KSywuE8KxdV1mwOB1EVL9DvnTz4I26TJjfO9jKQUEhK9kJRCQqIXklJISPRCUgoJiV5ISiEh0QtJKSQkeiEphYRELySlkJDohaQUEhK9kJRCQqIXklJISPRCUgoJiV5ISiEh0QtJKSQkeiEphYRELySlkJDohaQUEhK9kJRCQqIXg0IpbpwPFSX+ExgUSiHv6/4HEoOWng0LVOobZ5de+WD4oNzNzWWgRZC4RoQMsWzQ5u7mPsCSnOPHnnllz84LxUWFVFVW4uPri1KptO0Qdy0EUiqV+Pj6ceLYUcCy0U1rcxNOOmdKzxRL+0Dd4JjNZvR6PfYOjqTt2Q3Aceu9NnR1UllZifw63WOZNXZKZUUFTlotwyKjLrrV6QX07Io2c1riFW/O25efEoTOXi2cNErhpFEKrZ1KyK7j9aXftf9pFJZ77KCSC62dStir5AMqT0ig/2XtEGhT18KCAq4nJqC5w4BWq0Wj0dDSaURcVwkkrjVd3ZZ77O7uTkun0RYDY6AoKim7rHw2pXB2drYl6uzV38vopr0wbqi98vsmSN0rydvd5Ue302xpaaGuuc12rLmIVVXLevYStODpqruojOfjpFHirnO0HV/MYCqt+XrQ2qnwcnP+Xj55r79757mYI9C7vS5Wbu+hp5ebM3bnNdjFZNbZqy9oe72L9nv3QtVLJg9npwvaAr5/rxxUcjycL4wodbF7d758jmrFRevV+7zW1tYfLddRfWGqt/v3x5kXa6/zz7vYfXBxtLOd56i5vMG+7Yl48eVXSE1N4UhGBu3t7QQHB+Pm7o6Pjw852dkkr1/PQz+7j58tXcpHH37I+nVrefSBpYwZM4bDGYepqqqisrICPz8/br/jDjYkJ/PO8vdZcutCfvfYYyQnJ3M4IwNPTz06nY6IiAjq6xtYvmwZ0TGhPP3Xv3Jg/36WL3uXGTNmMmv2bAoLC6muqqKwsBCDwcDSBx+ivb2dR371KAF+3nz65lsUFxezOzUVmVyGRmNHWFg4wSHBvPryyxQVFvLB8nfR6XQ89+yzuLu7kzRvHt3d3dTX1XHq1CkOZ2TwX0uXkpg4lV8/+ivy8gt5/dWX8fXzY8f27TQ2NNDR2UFwcAhTp05j5Refs+q7NfzmVw9zxx138f77y8nJzmHa9Om4e3hgMhopLChkw4b13Hf3XTz669/w9ttv8ukXX/Hg/fey+LbbSEtLo7KygqrKKjw8PLhtyRL279vHi6++xpwZ0/jzX/7CurVr2b5tG/Gj4/H19UOr09HU0Mhnn65Aq9Px4ksvk5l5gj8+/iTTJk/kkV89SkFhAWfLyig5c4bm5mbuve9+7O3teeSXv0Cj1vDNV1/S0NjA2tWrUSgU6HQ6AoOCCA8P58MPPmD//v386+UXGTp0KM89+yzd3SZuX3InSqWCqsoqzpaVcvTYUebNX0DSvHn8+YnHST90hH/89S9Ex4wkef06aqprkCvk+Pr6MXXaNNauWc2nX3zF0vvu4ee/eJiPP/qQ9PR0ZsyciY+PLx2dHVRWlLNz+w7GjE3g4V8+wmcrVvD+xyv46V1LuPe++9mblkZZaSn19fU4OTmxaPGt5J/O589P/5XRsTG89PIrpKaksHr1d8THxxMUEoK9nR3tbe189+03tLe3cduSO0icepkBhXr7Uys//1Q889SfxY5tW0VjgyXkb+bxoyLQ11tkHNgvhBDi0IH9IiE+ThgNnbbzMg4cEE898bjYsH69EEKIutoaAYjl77xty7P83XfE5ys+EYcPnQtfGxkWKh777W9sx7OmTxUbk9fbjlubm8Rzf/+rePrPT9jSVDJE4qTxtuM1330r3l++THzw3jJb2k/vulN4uOhsx08+/ifx2isvXVDX5e+8LeKiR9iO71pymzi/SUpLzoivv1opXnz+OVFfV2trH0BUV1YIIYTYsfQAkUYAABDUSURBVH2reOrJx0Vn+7ko9Xk52WJIoL9IXrdWCCHE7tQUAYjDhw7a8hw6eED8/ZmnxcrPPrWlAeLvzzx9gcwHD6RfIPPEsQnip3fdccE557dNS3OTePnF58Wf/ue/bGl+3p62QDJCCLHi4w/Fv//1ivjsk49taU/86Y/CXqWwHb/4/HPi6aeevODaG9evE/Nmz7QdP/7H/7mgvfJys8V7y94RLz7/nDhTXCSEEGL/vr0CsIUszjpxXPz20UdEfW2t7byqinIxY+oU8cWnK4QQQhScPiUAsW7Naluew4cOihee+8cF9xgQv/7lw7bj/37s92J3asoFMi9euEDMmpYoroTvTcn6BwSi1+vZvm0bu1JTrYoDJeWVHMrIsJgXlYrg4BB27thpC1AyZGgo69atIzl5vSWPNSRUfX29rezo6BhOnjrJihUrbGn5+QUcOHDAdhweMYza2lrbGMdRqyMzM5NPPz13TmBQIObzxJ6SOBUQfP7ZZ3R2WGKqtbW1UXvexs3BwSHIFUpSU3baArAYTSaOZmZRcPoUAAEBgehdnSnIP21rC3d3D7768ktSU1KsJVn8jiNHLMFOHB2d8PHxZePGjbYZFnt7BwpLyjh08CBgCcjoqnPixIkTNnmiooazc+cO1q5dc0H7V1ZWAtDV1Wlpr7yTrDsvz+nTp23lAowaGU1LSytNjY0AOGl1lJaU8MknH9vy+Pj4oFKdcx2GhoWjUqv59ttvqLZer66ujg5jN4auTgB8/fyxs7NnV0oKnZ2WtPaODjZu3U763jRLHn9/7FRy2yyil6cXer0nmzdtYveuXcC5ADXZWZZ4It3dZkKGhJKSspOMjEMAuLi6sit1N+nplsAxWp0OnYMdZaWl5+oZH8+BAwf4etWqC9urqtL2d9yoUZSWlrJuzWpbWkF+Punp+7gS5L03w/Xx8cHTy4uNGzewffs2ADR2dgAcP34MADs7OyZPnsyJ48f55OOPAHB1cycrK5v9VgFkMhlDggIoryjn+NEjCLOZcRMmkJeXx9o1a88JoJBTW1sDgLm7m5mzZlFfX89bb76ByRrfraa2hsIz5wZJCQkJeLi7s3b1d5wtK8XVzQ1zt5mdu/Zw7KjlBjlpnZADRw9bFDkyMgo3NzdWfPIxe/dYbmrPtOD+9P0ARMdEM27CBLZs3sy+vXsBCAgI4PCxE6SlWc5xdLT45oWFhRi6unDWORMWFsaG9etZt9ZSLycni29+7JilvVRqFfPnL6C4uJivV30FWAK65OTkkGaVBSB8SDAdHe0UFuRTfvYso0ePJiszk3feesuWRyaD2tpa23HSvPmo1Wpe+9erNFg7oMamJipr6mlusijKyJGx+Pn5s27NavJycxk/YSJyuZzV65LJsLaPo5OlXqmpFuUPCQkhODiYlSu/YJc1TWkN2HnqlLUT8Q9g4sRJ7E3by66UFFzc3AkPDydl1x62bdtqOccairi8vBxh7sbOzo7o6Bh27tzJ119Z2kKtscME5ObmWO+Lgrnz5lFSUsKXn39mrbicgoIC9lineAFGREZg7jZTWJDPmeIiRsXHU1ZayltvvmnLIxC0dhopLMjncrlgbCKTyQgdGkZsbBzHs3I4dMDSIw0ZMgQvDzccHR2pq63BycmJKYmJVFRWsH3bNtv5Li467KwKpNXpSEqah4O9A/vT020LJp0dnRSXnnvA5yYlETFsGGl7dlNaWsrs2bNxdHJk27atFBUVAeDv54+jRkVHu2VAPnvOXIYPH8HetDRKSkoAbGGjeqJvJiZOJXHKJDIzT5Bx6CATJ08mIDCQ1NRUMrMyLeX6+1vOsVoXLy9v5s6dS1ZmJsesYa/cPSxxhHsUdEhoKPPnzqapqZGtWzczLCqKmbNmk5OTw+5dFsvq5uFBgI8XHh7utLe1IpPJuGXhQtrb29iQnGyru1arRWN3Lnb3nLlJeOj1pKakoFapCA0Lp6WlhR3bt9vyzJg5i9i4OI5kHKKwIJ/Zs2fj4+PD9q1bbTfe28sbgNYWywB32vTpxMXFceTwYcrLzwJgb22v2ppqACZNmkxCfBxlpaUczjjEuHHjiYyKYn/6Pvam7bG1D4Dc2pF6eXkxZ+5cTp8+xZEjhwEYGhaGAM4UFwMwLDKSOTOnYzAa2JCcTFBwMDNnz6a4uIiUnTtt9QoJ9LeVL5PJuPXWxSiUCjZu3GjLY+9gj0JxbmJk9pw5+Pn7kWq1ZpFRwzF1d7Ntx06qrBZwSuJU4qKHc+L4MUpKznA5XHQFpSeEVanVfClVahYuXIi9vT2bNmxArVYTExtHbU0Ne/ee6+mGhg7F3d2ycmk2d5M0fz4ODg6sWbOahgZLL+Zo7UWxul1J8+YRFRlF2p49nDlTjIOjE0qFkszsXM6etSjP0KFhREZG2Xqo2Lg4QkND2bUrlVJrRXXWqJwtLS2WmzEsktmz53Ds6FEyTxwHICwsjKIzpeRkZ9vqOXvGNNraWtm6ZRMhIUOYNGkyebm5th7J1c0dJzuNbcHHy8uLJXfcQV1d3bkHXCajsqqSvNxcW1vMnTcPNzc31nz3HSaTiUW3Lqa1pYWUnTtseUJCQtDrPW3HSfPmodfr+e67b2lqtrh+JpMJo4Bqq5swc9YsoqNj2Ls3jZN5eUyZOg2tTkva/gO2DiJ06FAihg6xdSrDR4xgRHQ0u1JTKCq0uKXOLq4ANDQ0AJbA9PMXLOD0qdMcSN+PXKFg2LBh5GTnkJeXB4CPtw/xI2Mwm810m4wEBAYyfvwE8vNP2yyMSm1R8lbrfdDpdNx+xx10dnSyITnZ5nXU1tTaLAPApMmT8fHxIS8nh87OTmbPmYPJZGLH9m001FtCwAUEBOLr64vRaAkAM3v2HEJDQ1m/dq1NCVQqJQIoLbW0RWLiVBLGjuPUyVM2F+7HuKhSqNRq5Fz4vsr8+QuQyWSs/HKlLWxtZWUlxaVnbXlmzp7NkNChpOzYTklJCfMX3IJao2bzth2cOG55MCOHRRIzPIqTJ08CFtMeFh7OurVrOFtmUQKZ9WWo6qoqAMZNmMC4CRM4mZfH/vR9xMaNYkhoKAcPH2XnDktvExgYyMgRUXR1ddFtMhEYFMToMWPIyMhgQ/IG6w2yTB9WWR+w0NChzJmbRGlpKRs3biQsIpyY2DgOHTrIpg0bztVr1ix0OmdKiovp7u5mztwkKisq+O6bb2x5zGbzBTGi581bgJOTlq+/XoXRaERjZ0ddbR0lZytsD/iUxGkMHz6cHdu3UVhYQNL8BWi1WjZs2sKpk5YOQOdsUfYya9vEjBzJyJEjWb9uHYVFloAoDg4W16enE4uKGk7i1KmUlZaQvm8vsXGjGD16NKlp+9i0wdLzDrHG1GtrtVhfX19fJk6cRFZWJsnJlhDQGjt7jALOnrXc46DgYOYkJdHR2cHmzZvw8w9g0pREsrOzWJd8rkcP8PXGQ6+nvraGtrZ25syeS2trK1+vWkVDXZ21vbpp7eiynTM3aR7+AQGkpOykubkZdw89ba2tlFfXkn/aMsZLnJJIXFwcKTt2WKzknDm4uXuwJnkDhYUXtkXPsxMeEcH4CePZs2c3KTvOdUg/xCXX2qNHROHt7U3pmTMYu7qYOm06Wicte3bvprbG4tP2xEyusPbo06fPICYmhkMHD1JTbTHLzi6WB7HHDx4VH09CQgLFxcXk5eYybvwEfP38OHLkCHl5lp5Wp7WU2/OQ+fv7M3PmTHKys2298dCwMABqrObf28eHWbNm09nZSXr6PoKCg5mSmMjZsrM2y2CzUlZXzsHRkclTptDS0sKu1FRbUEeFQkFLW4etLWbNmYOXtzeHDh3E0GXAx9cPs1lQXd9Ie5vFRQkMCsLTy8vmjkycOBG9Xs+u1FQarYNgVzdL79zTo0+eMoUxY8eSlZlp6+l62rTJOh4ICgrGw9WZM2fOIISZ+NFjGBIayvHjx8nOstTL29vidtRbe1S/AH+S5s2nsKjoArcGoKra8rC4uroSHTkMg9HAwf3peHv7MG36dGprazluHQsBKGXnRSGSyUhKmgfILnDp5PIL1xgmTbL0+mlpaTQ01BMYHIydnR11Tc3UWz0GPz8/PN1dKSm2WLP4+HiCg4NJ27PH5lW4Wd+X6gkiOSo+ngkTJlJQkE9ZaSkyucLmcvUoroeHB/ZqpSUYJZZON2r4CE6dPHnBRMcPcUmlmDp1GmFh4ezda/HbnV1dcXR0pKW903ZTR4yIJjQ4kOzsbBoa6okYNoywsHAOHzli01xXFzcAmq3uQEjoEOYkJZGbm0NmpkXIkJAQukxmcnMs5tTX149hYUOprq7mZF4unp5exI2Kp7S0jAP7LYPiHndJbr1hGjs7Ft56K42NjWzfZrlhao0dbW2tFFsbHmDOrBnonF3YtzeN+ro6xiSMxdBl4NiJLKoqKwCIi49nSEgQRYUFCHM3kydPxsvLk61bt9JiXYhycLD45D2uxZTERGJiYti1axf5p0+h9/LCQ+9BQ0sbxVY3JjpmJB6uOsrPnqWttZUhQ4YwfPgIjhw5Yrthbq6W9qqwKknEsAhmz5nDqZMn2Wnt6aJjYqiuayDTeo5/QADBAX4YDUbyT5/CycmJMWMSqKqq4sB+y8yeSq3BQa1ErbG4N11GI7PnzsHQZWDfvn3I5HLkCiVtbW2UV58byM9Nmouvry970/ZwtqyMSVOmoFIqSd+XTol13DBixAg83V0pLT2D2dzNlMRE/Pz82b17t+3h7Bk75edbxj3jJkxg7NixpKfvJy83l4hhkXh5e3P8+HHyT1vyREZF4WSvobWtFZPJiK+/P6NGjyYrK4vDVmV3c7e0V7VV2X39/Jk3fwGFBQVs3bwJZDJGjYqnuLjY9nz9GIpnnnnmmd6J3SYTDg4OBIeE4OXliY+vL05aLd3d3RQXFnD7kiX4+Pqi0Wjw8PAgNjYOJydHPD09kSsUtLa0Ehc3yhq21kRDfS3zFywgMDAIpVKJs7MzCrkCL28v/P0DUKvV5GZnMW3GTBLGjkUml2FnZ8+o+FHoPT3x1Hvi6upKTU0Nfn5+jIqPR6VW0dTQwLjxE4iNjUOhUODg4ICDgwMKpYLomBjA4uJFRg1nwS0LAcsM2/Dhw/H29sZD74laraa1tQWZMLNo8WIcHBzo6uoiLCycuLg41BoNzs7OaDQaujq7iI2NRavT0dXZhaGzg4WLFuHm5o69vT3+/gF4+/ri6eWFVqvDZDJRWHCa226/neDgENRqFc7OLoxJSMDRyRF3N3fUGjWtra1ERUURHBxCd7eZyopybr31VssbpkLg4+uDr58fbm7u+Pr64uDgyKncHCZMnMiUxETkcjlKhZIxY8bg6eWNm7sbbm7uNDQ04ObmZgt33NDQQEJCAuPGj6fb1I3e03JvHZ2ciIy0hE2uqa3Bx8uL25fcYWuvYcMiCQgIwN3dHXsHB4RZYDAamTh5Eo6OTnR1dRESMoRRo0ajVCnR6XT4+vqiVquJihqOztkZmQwqK8q57bbb8fL2xt7ODh9fXwIDAvHw0OPs4oxMJqOpqZGJkybh7x8AyNBqtYwdNw5HJydcrB1zW1sbgYFBhIdHIENG6ZkikubNZ/jwESAEer0ngYGBuLq54efvj1wup6SkhJEjRzI3ad6PKoVM9F6okJD4D+d77pOkIxI3Oz/2jEuWQkKiF9LXPBISvZCUQkKiF5JSSEj0QlIKCYleSEohIdELSSkkJHohKYWERC8kpZCQ6IWkFBISvZCUQkKiF5JSSEj04v8BFlwNyV4DdccAAAAASUVORK5CYII=)
physics-General
physics-
A hollow sphere is released from the top of a wedge, friction is sufficient for pure rolling of sphere on the wedge. There is no friction between the wedge and the ground. Radius of sphere is R. At the instant it leaves the wedge horizontally. Angular velocity of sphere
is
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)
A hollow sphere is released from the top of a wedge, friction is sufficient for pure rolling of sphere on the wedge. There is no friction between the wedge and the ground. Radius of sphere is R. At the instant it leaves the wedge horizontally. Angular velocity of sphere
is
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)
physics-General
physics-
A uniform hollow sphere is released from the top of a fixed inclined plane of inclination
and height 3m. It rolls without sliding. The time taken by the sphere to reach the bottom is
![](data:image/png;base64,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)
A uniform hollow sphere is released from the top of a fixed inclined plane of inclination
and height 3m. It rolls without sliding. The time taken by the sphere to reach the bottom is
![](data:image/png;base64,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)
physics-General
physics-
A uniform hollow sphere is released from the top of a fixed inclined plane of inclination
and height 3m. It rolls without sliding. The speed of the point of contact of the sphere with the inclined plane when the sphere reaches half–way of the incline is
![](data:image/png;base64,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)
A uniform hollow sphere is released from the top of a fixed inclined plane of inclination
and height 3m. It rolls without sliding. The speed of the point of contact of the sphere with the inclined plane when the sphere reaches half–way of the incline is
![](data:image/png;base64,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)
physics-General
physics-
A uniform hollow sphere is released from the top of a fixed inclined plane of inclination
and height 3m. It rolls without sliding. The acceleration of the centre of mass of the hollow sphere is
![](data:image/png;base64,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)
A uniform hollow sphere is released from the top of a fixed inclined plane of inclination
and height 3m. It rolls without sliding. The acceleration of the centre of mass of the hollow sphere is
![](data:image/png;base64,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)
physics-General
physics-
A mouse, searching for food, jumped onto the rim of a stationary circular disk mounted on a vertical axle. The disk is free to rotate without friction. The velocity of the mouse was tangent to the edge of the disk before it landed. When the mouse landed, it gripped the surface, remained fixed on the outer edge of the disk at a distance R from the center, and set it into rotation. The sketch indicates the situation The mass of the mouse is m = 0.10 kg, the radius of the disk is R = 0.20 m, and the rotational inertia of the disk is I = 0.0080 kg·
. The speed of the mouse, just before it landed on the disk is
= 1.5 m/s. The mouse, still searching for food, crept to the center of the disk (where r = 0). Find angular velocity of the disk plus mouse, when the mouse was at the center of the disk.
![](data:image/png;base64,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)
A mouse, searching for food, jumped onto the rim of a stationary circular disk mounted on a vertical axle. The disk is free to rotate without friction. The velocity of the mouse was tangent to the edge of the disk before it landed. When the mouse landed, it gripped the surface, remained fixed on the outer edge of the disk at a distance R from the center, and set it into rotation. The sketch indicates the situation The mass of the mouse is m = 0.10 kg, the radius of the disk is R = 0.20 m, and the rotational inertia of the disk is I = 0.0080 kg·
. The speed of the mouse, just before it landed on the disk is
= 1.5 m/s. The mouse, still searching for food, crept to the center of the disk (where r = 0). Find angular velocity of the disk plus mouse, when the mouse was at the center of the disk.
![](data:image/png;base64,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)
physics-General
physics-
A mouse, searching for food, jumped onto the rim of a stationary circular disk mounted on a vertical axle. The disk is free to rotate without friction. The velocity of the mouse was tangent to the edge of the disk before it landed. When the mouse landed, it gripped the surface, remained fixed on the outer edge of the disk at a distance R from the center, and set it into rotation. The sketch indicates the situation The mass of the mouse is m = 0.10 kg, the radius of the disk is R = 0.20 m, and the rotational inertia of the disk is I = 0.0080 kg·
The speed of the mouse, just before it landed on the disk is
= 1.5 m/s. Find the magnitude of the impulse received by the mouse as it landed on the disk.
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)
A mouse, searching for food, jumped onto the rim of a stationary circular disk mounted on a vertical axle. The disk is free to rotate without friction. The velocity of the mouse was tangent to the edge of the disk before it landed. When the mouse landed, it gripped the surface, remained fixed on the outer edge of the disk at a distance R from the center, and set it into rotation. The sketch indicates the situation The mass of the mouse is m = 0.10 kg, the radius of the disk is R = 0.20 m, and the rotational inertia of the disk is I = 0.0080 kg·
The speed of the mouse, just before it landed on the disk is
= 1.5 m/s. Find the magnitude of the impulse received by the mouse as it landed on the disk.
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)
physics-General
physics-
A mouse, searching for food, jumped onto the rim of a stationary circular disk mounted on a vertical axle. The disk is free to rotate without friction. The velocity of the mouse was tangent to the edge of the disk before it landed. When the mouse landed, it gripped the surface, remained fixed on the outer edge of the disk at a distance R from the center, and set it into rotation. The sketch indicates the situation The mass of the mouse is m = 0.10 kg, the radius of the disk is R = 0.20 m, and the rotational inertia of the disk is I = 0.0080 kg·
The speed of the mouse, just before it landed on the disk is
= 1.5 m/s. Magnitude of the angular velocity of the disk plus mouse, after it landed becomes
![](data:image/png;base64,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)
A mouse, searching for food, jumped onto the rim of a stationary circular disk mounted on a vertical axle. The disk is free to rotate without friction. The velocity of the mouse was tangent to the edge of the disk before it landed. When the mouse landed, it gripped the surface, remained fixed on the outer edge of the disk at a distance R from the center, and set it into rotation. The sketch indicates the situation The mass of the mouse is m = 0.10 kg, the radius of the disk is R = 0.20 m, and the rotational inertia of the disk is I = 0.0080 kg·
The speed of the mouse, just before it landed on the disk is
= 1.5 m/s. Magnitude of the angular velocity of the disk plus mouse, after it landed becomes
![](data:image/png;base64,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)
physics-General
maths-
If AB makes 90º angle at the vertex of parabola then -
If AB makes 90º angle at the vertex of parabola then -
maths-General
maths-
The ends of a line segments are P (1, 3) and Q (1, 1). R is a point on the line segment PQ such that PR : QR = 1 : λ. If R is an interior point of the parabola y2 = 4x then -
The ends of a line segments are P (1, 3) and Q (1, 1). R is a point on the line segment PQ such that PR : QR = 1 : λ. If R is an interior point of the parabola y2 = 4x then -
maths-General
maths-
The circle x2 + y2 + 2λx = 0, λ
R touches the parabola y2 = 4x externally, then -
The circle x2 + y2 + 2λx = 0, λ
R touches the parabola y2 = 4x externally, then -
maths-General
maths-
If b and c are the length of the segments of and focal chord of a parabola y2 = 4ax. Then the length of the semi-latus rectum is -
If b and c are the length of the segments of and focal chord of a parabola y2 = 4ax. Then the length of the semi-latus rectum is -
maths-General
maths-
A parabola is drawn with its focus (3, 4) and vertex at the focus of the parabola y2 – 12 x – 4y + 4 = 0. The equation of the parabola is -
A parabola is drawn with its focus (3, 4) and vertex at the focus of the parabola y2 – 12 x – 4y + 4 = 0. The equation of the parabola is -
maths-General