Question
An observer can see through a pin–hole the top end of a thin rod of height h, placed as shown in the figure. The beaker height is 3h and its radius h. When the beaker is filled with a liquid up to a height 2h, he can see the lower end of the rod. Then the refractive index of the liquid is
![](data:image/png;base64,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)
- 5/2
- 3/2
The correct answer is: ![square root of left parenthesis 5 divided by 2 right parenthesis end root](data:image/png;base64,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)
The line of sight of the observer remains constant, making an angle of 45° with the normal.
=![fraction numerator 1 over denominator square root of 5 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACIAAAAqCAYAAADWFImvAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAATNJREFUeNpjYKAMqAFxLRBfYBhgsBiI04D4P8MgAaMOGXXIqENGHTLkHfIfCx4Fo2DkgP8DhEfBKBg5gGew5JYIIN4/GEJkOxCnDLQjRID4PZQeUJABxOtJLJ1pAkBpI2SgW2oKQPwaiDkG2iEVQDx7MLRdzwOxBz0dwoNFTAeInwMxCx6H/ALiT0C8DYiLcJhDFFAB4vlQQ23Q5NqBuJ8IM0AONWaADOLcAGINchxSA3UIqJw4hSZ3H4hNSDTPDYgPUhI1WUD8D4jFoXwLIL6NJ1rwgR+UppNvQLwMyp4MxA1kmAFKV3cpdcgcIP4ODYXXRMT1OiC2BGImKPaAOiKIUocIAPFfIF4LxMeJUB8KxLeA+A8QvwPiVUBsSq1sfBiagwoGuoIzhTpEZjC0PUJobQEAJp93i2JeaO0AAABxdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4xPC9tbj48bXNxcnQ+PG1uPjU8L21uPjwvbXNxcnQ+PC9tZnJhYz48L21hdGg+p6dYKAAAAABJRU5ErkJggg==)
![mu equals fraction numerator sin invisible function application 4 5 to the power of o end exponent over denominator sin invisible function application theta end fraction](data:image/png;base64,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)
![equals fraction numerator 1 divided by square root of 2 over denominator 1 divided by square root of 5 end fraction equals square root of open parentheses fraction numerator 5 over denominator 2 end fraction close parentheses end root](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/900247/1/950469/Picture14.png)
Related Questions to study
A diverging beam of light from a point source S having divergence angle a, falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is t and the refractive index n, then the divergence angle of the emergent beam is
![](data:image/png;base64,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)
A diverging beam of light from a point source S having divergence angle a, falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is t and the refractive index n, then the divergence angle of the emergent beam is
![](data:image/png;base64,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)
A rectangular glass slab ABCD, of refractive index n1, is immersed in water of refractive index
A ray of light in incident at the surface AB of the slab as shown. The maximum value of the angle of incidence amax, such that the ray comes out only from the other surface CD is given by
![](data:image/png;base64,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)
A rectangular glass slab ABCD, of refractive index n1, is immersed in water of refractive index
A ray of light in incident at the surface AB of the slab as shown. The maximum value of the angle of incidence amax, such that the ray comes out only from the other surface CD is given by
![](data:image/png;base64,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)
A smooth block is released at rest on a incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is-
A smooth block is released at rest on a incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is-
A block is kept on a friction less inclined surface with angle of inclination . The incline is given an acceleration a to keep the block stationary. Then a is equal to-
A block is kept on a friction less inclined surface with angle of inclination . The incline is given an acceleration a to keep the block stationary. Then a is equal to-
If the sides a, b, c of a triangle are in G.P. and largest angle exceeds the smallest by
, then ![c o s blank B equals](data:image/png;base64,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)
If the sides a, b, c of a triangle are in G.P. and largest angle exceeds the smallest by
, then ![c o s blank B equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADkAAAANCAYAAAAT88Y+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAaBJREFUeNpjYBg84AcQ/wHih0B8F4g3AbEkwzACKkB8AU2sGYjnDydPBgDxUjSxICxiVAE8QNwFxE+B+BcQrwNiQSR5USCeC8RfoMlrIRBzYDGnGprsQMnvPxCXE7C3HosakNketPDgOSBuBWI+IGYD4hIg9oHKgzx7CYgTgZgJqmY5NFDQPTgbqp9YsAoamyBzDaABWYBD7X8iME7QAcST8MiDPFOEJqYExLfQxI4CsQuJAXwLyYFfaBGDDNAQfI2WNLHJoydNEP8DmlgoNEX4kWD3FyibDRpAx4FYjdqeNAXiw3jkjXHImwPxfiziklD1+6HZAB8AmbEXTSwaSzagOLl6QQsZXMAPmm/QQQE0D2MDHNA8HEvAk5HQPIgMYqH5mqoAFFM38MiD8sg2LMnsGhBr4NE3Fxor+MAkaGGGri+SFvnyAjRWWKAlJyiWrKFyLNBqBVbSSkNjvppAFgAFgjABe9chFTSi0Dx9gcTSmWggC8QHoXUbKJklo8nbQh39CxrriVjM+ADNE3+g+VGDCHvfIeWlH9BqSZphFJAGABGuZl9f52v0AAAAgHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5jPC9taT48bWk+bzwvbWk+PG1pPnM8L21pPjxtaT4mI3hBMDs8L21pPjxtaT5CPC9taT48bW8+PTwvbW8+PC9tYXRoPgKIcpsAAAAASUVORK5CYII=)
Two plane mirrors. A and B are aligned parallel to each other, as shown in the figure. A light ray is incident at an angle of
at a point just inside one end of A. The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (including the first one) before it emerges out is
![](data:image/png;base64,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)
Two plane mirrors. A and B are aligned parallel to each other, as shown in the figure. A light ray is incident at an angle of
at a point just inside one end of A. The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (including the first one) before it emerges out is
![](data:image/png;base64,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)
A point source of light B is placed at a distance L in front of the centre of a mirror of width d hung vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance 2L from it as shown. The greatest distance over which he can see the image of the light source in the mirror is
![](data:image/png;base64,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)
A point source of light B is placed at a distance L in front of the centre of a mirror of width d hung vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance 2L from it as shown. The greatest distance over which he can see the image of the light source in the mirror is
![](data:image/png;base64,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)
Figure shows a glowing mercury tube. The illuminances at point A, B and C are related as
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ0AAAB3CAYAAAAZ3BUbAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABa0SURBVHhe7Z0JtFVjG8ffkDlkjKRQaZSEkqJJiMxRxlokY4YMS4bUqpa0SmqRDCFUSGQIEUnGkiZjJClTFyFUhu/ze9q7brdz79n7DPues8//t9Zedc+w7737nve/n+l9ngr/+w8nhChYVq5a4/0vGJt4/wohRCDStjR4+8qVK11RUZFbvny5+/vvv71nhBC5wLbbbut22WUXV7lyZbflllt6j64nrKWRtmj8+++/bv78+XYsWbLE/fXXX94zQohcYIcddnC1atVyDRs2dNWqVfMeXU/k7sk///zjFixY4BYvXizBECIHWbFihVu4cKFbunSp90h6pC0aGCqLFi0y8RBC5CYIByGETKBAaMyoUKGC23TTTd1mm21W7scmm+jjFUfSjmmsWbPGDRo0yGIbxdliiy3sgyOiBcEg8IXll+afNi34OQiKr169WlZoObBq1aqNrvuBBx7oOnbs6H21nsgDoaWJxgknnOAOOOAA7ysRJZ988ombPXu2+/XXX8tFOBCM6tWru/3339/tvvvu3qMiSh566CGLMxYnU6Ih+zGGECknSo61FzUIxvbbb+/22Wcft9tuu3mPijgh0YghLFzu8jvuuGO5xBVq165toqWYRjzRXzWmVKpUydWrV8/ttNNOkS1exKo8rRwRDRKNmIJQ7LXXXhZbQECyLRycf9ddd3U1a9a0YiKyOCKeSDRiDHd7XIUqVaqYFZBNNt98c1enTh0TDmXN4o1EI+b4Qcmdd945a3d/zrvvvvu6qlWryi0pACQaBQCWxt57720Ckmk3BcEgS4JFs/XWW3uPijgj0SgA2NlIbIMjk5YAAoRQNGjQwAKu2XaBRG4g0SgQCE7WqFHDtkhnCkQC1wcxqlixoveoiDsSjQICwWCRk01JF6wM+jM0atRIglFgSDQKCBb3nnvu6erXr29ZjnQOysMbN25s+1yUXi0stPdEiBiivSdCiJxBoiGECIVEQwgRComGECIUEg0hRCgkGkKIUEg0hBChkGgIIUIh0RBChEKiIYQIhURDCBEKiYYQIhQSDSFEKHJulyvn+fPPP90ff/xhU+hLnleIQoAGR3RZ22abbaxpc9j2A9nc5ZpTosE5vvnmG/fMM8+4CRMmuLlz59poQbWRE3GHZcjsW3850ne1ZcuW7rzzznPNmjVz2223XSjhKBjRmDNnjhs4cKB744037GsavRxxxBGubdu21vhFiDjCoOYvv/zS9e/f3xUVFZk4cKNkFATWRu/evd3JJ59sjaGDUhCiwdDim266yX377bfupJNOcgcddJCbN2+eWR2YaJdccokN4hEibixatMhulvPnz3dNmjRx559/vrkkjz32mN1AGa/Zt29fd/zxx3vvSE5BiMZll11mF4pfijmkdLkmrrFgwQL33HPPuRUrVrgBAwZ4rxYiHvAZf/XVV12/fv1c9+7d3YknnmgzaujB+tNPP7mpU6e6Bx54wLVv395deOGF1q4xCLEXDdR0+PDh7txzzzVXZKuttvKecW7VqlXu9ddfd6NHj3Zdu3Y1P0+IuPDhhx+6IUOGuGXLlrnx48dv1C2emyXuCQLQs2dPE5UgZFM0ciLl+sorr5h1Ubdu3Q0EA5jZsd9++9nz06dPN2tEh464HL/88ou5JwQ7ieERxyh+YHUceuihdnNeunSptyrKl5wQjY8//tjG+uG7JYKZHcQziHuUvKg6dOTzQcaE0gJiGQQ/Ex3cMFkDuDK5QNbcEy5GycdKA7OMdviMDkR969WrZ24IU8+B74ELc+2117r333/fHhMiDjz77LOWABg5cqRZFCxHLGoOXHP48ccf3bRp08wSad68uT2WjOXLl9vUu2rVqtmYCahVq5Z9j5JE7p4QsOEH4ZcpfmA1sNiDHFwoBAbF5evi+eri+K/ToSMuB/AvVoT/+ebzv3r1ahMNDlwY1gXP+Wsm2YGrz7o87LDD1h2Zyj6mbWlkgk6dOrnTTjvNIsSJctFctJdeesmNHTvWPf74496jQuQ/U6ZMcddff70VcV166aXeoxvy4osvumHDhrkOHTq4q666yns0c0SePckEN998swVAO3fubC5KSb766iv36KOPup9//tleK0RcePfddy3diit+7733ukRVn0OHDrWbJtnDbt26eY9mjrwUDfy1UaNGWcq1VatWljHxwUzDv7vnnntcly5dXIsWLbxnhMh/SLWOGTPGvfDCC+6RRx5xtWvX9p5ZC8WO11xzjZWRX3HFFVb0mGnyUjSAC4JYHHfcca5BgwZmebBx7aOPPnKTJk1y3333nevTp4/3aiHiA7UaBPmxsm+55ZZ1xV1Y1lgfb731lrvuuuvsppkN8lY0SLtiphH1pYCFbMrs2bPduHHj7Hl8PiaeCxE3Vq5cadnBO+64wzIdxC34l0pQNnD26NHDPv81atTw3pFZ8lY0AFMNE+3JJ5+0OAbRYjIqXFQhCgksDeIcvXr1ss1q7HrNFnktGn5KqWQfjRz6EYWIDISDXa7ULoXtpxGGvBYNIUT0hBUNtfsTQoRCoiGECIVEQwgRComGECIUEo0YQ+cn9i189tln3iPZ5YMPPnAzZsxwP/zwg/eIiCMSjRhC2poWAhTGTZ482appo4DCPBoqTZw40TrJ50r/B5FZlHKNEfwp2RFMdeHLL79si5bt0UcddVTg3pJlwbmpUKQhDL0dSoJo8H3fe+89qy9o2rSpff9ErxW5g+o0ChD+hGzso23czJkzrRHzHnvs4c4++2zXsGFDW8Al4T3s7cEKoS9lpUqVvGdK5/PPP7fu8HScOvXUU+17JAI3hcpezs0IisMPP9yqG2kWLXKPsKKx6S3skBF5CzMz6OzEPp377rvPvf3229bq/uKLL7a9OizwkiAYDKGaNWuWe/rpp21PA12eilcdEg/hdRUrVvQe+e8O89/z33//vZX5//7777bBij0SJasVsSwOOeQQEyt2KDPPhvNUrlxZwpGDrPn7H+9/wZBo5CksaGIXS5YsMcvirrvusgU8ePBgu7uXtjh5H3t5EBfaDfD1KaecspE1QsMjnivu1rDzmF6u1atXt/4muCr+juSSwsFjtG2sU6eO7eLk9WwN4L0ISCIxE+VDWNGQe5KHsPi402MpsBOSzX3sgjznnHO8VyTGFwxGQjCIh5b2DOZJ5JqwSerYY4+185aEdnS4KldffbW5HTRGYgIeeyUSwc/6zjvvmEixr+jyyy83S4RWCNncUyGCoTLyAoDdwDSipU0cFgXxA+IXycAlefjhh92tt95qQUp6mASJZZQEK4GxEmRncI2uvPJKszpKgwl5bdq0cSNGjDCxoL3jbbfdpuxKniLRyCMIXOKK0LAF94LFijtStWrVpHdsYhEMnKKhC0N3sCDSucvzXtwhrAe+Pz0gyJpgSSSC19NchlgLHbipHaEvLClhtT7ILxTTyBNwB+6++27LXjAHg9m23LWxFJItfoYL0wGKc3CXP/LII+3uXxa4L7Sew4UpDb4vLgaT9GhLR30GsQxEJFHGhtezzRtXhu7YBHH5nb7++msL2hIoFdGjQGjMwIQnw0FmhFgCQUuyIwQUWaDJwLJAMLBSGKzNPJkgLkkQ0fBBgGiPT+wCS4i2+8zbSCRMCAcDgOh5SfaFVvuffvqpNc7lZ6TZTDJBE5lFohEjWEzciUlbYlWw6JnERV0FCy8ZCAYzPXk9YoMABI1hhBEN4LwIBcJGgRel5ARJE42k8EEcsEpI+eLWMAiZto+kf6tUqeK9SmQbiUaeQ4aDOzbNlAlw8jVDsY8++mibkFW8U3tZ0N16woQJVoDFMG5/En9QwooGIByIANkdMju4HdRsIAKlQVAVUeN9VJpSEMZ7/QlhWCQiu0g08hjqLphXS3CR2gYW7THHHGMVlQQRk8UuANeA4CKxD8x/mjRTK0EsIQypiAYQHMV1Iv26YMECSwczbS9Zj0sEh5+XeAdZHgrCsDoQukyUwIvSkWjkIdyZubNinmNh0Lq+devWVqpNMVWioGJJsEiICfB+3Bne57+/eFVnUFIVDWCh45rwcyOCX3zxhVkMyfag4HIhLn4BGIKDi0ZaFzenLFdHpI5EI88g0MlsFwKImOUsLoZGIRosviDWBaLDwkIwpk6dagN1EAxM/iCxj0SkIxqAYCAc/D4sfKwG/s/PlAysFVwx3k9WhilkCAiuGe5WkGsigiPRyBNINxIsJFiJYHA3pvy7e/fuFlAMujAIPFJYhTuCW0L8A5fEH7iTKumKBhCvwLXAwkAY2R9DWhUXJJmY8bPzO5BdQSwQjoULF9pzfI2gpvP7ifVINPIArAsWAMN/OTDFqbto165dKFeCjAN7TxAMmu1goZx++ukJN5GFJROiAfwciAR1GLgq9Nsg8MmBqCT7OREIrA4qWKkzIbhLzIPfEXclFddLbIhEI4fBjSBewR2XzAh3X39HahCzvThshWcRUcNB/wwmjjPSMlN330yJhg+ZETawIXJsXiOlipgEmenB84hEs2bNzD2hiMx3d0jb4gql6oYJiUbOQmYEN+KJJ56wDz21CSx0XJKwd0vOheCwj4QMBRvHiIFkkkyLBrDAqR7F0mL/C24LIoA1EcQyQhDJsJBCpnfIgw8+6IqKikx8EBCEI8h5xIZINHIMshrELwhy9u7d2wJ67Cw966yzUhq1x7mwVFgwv/32m+1DOfjgg71nM0c2RAOwCpjTSw0G09CxQBCCoEFfwK1p3ry5ZYYI/r722mt2HuInEo7wSDRyDPzv22+/3d1///0Ws2BjF4smVV+ccmuqRKl9QIRYONlYJNkSDWBh46rUr1/fDRw40CwP4hZYC2FAJDp27GiuGtcXMSWInM25p3FEopEjEKSkhwQiwSKhhwS9OoOWgJeEhYVrQ9csROeiiy6yuEC2MgjZFA3g5yal2qhRI3PX2FTHgidjEhTEEvGleI0Dl42gMCLCz64gaTDCioaa8GQY3AfKp6nqnDdvnpV/c7AgUh3ki2AQOMXFwRXp0KGDxQOymXIsqwlPJqGCletEMyFclDPPPDMloeI81KqQwn7++edNMHADybqIslGP0HIEV4TiquHDh5vPfsYZZ7hWrVpZZoQPcaqCwS5V7qItWrRw7du3z7pgQLYtDR9/7wkpWdLQCCPiQVVoGDiPXzzG9aHClv03BEpTKaMvJGRplAO4IqQAaS7DhisqMkkPshDSMZGXLl1q8Qua/NIDgx4U6RZtBSUqS8MHC40UMteQKlCK1BBIxCAsWB1cO7qi09qQbBOtEPmbpHK+uCNLI2JwRfigs2+ElCJzPviw+5H8VEDHqRC98847ratV2E1rmSAqS8MHIeT3I32KdcCwJyw3LI4ge2+KgzAQKOa9bISjaxniwXlJ8aqadEMUCI0I7l60t3vqqadsgbPACHRiZaTTRIaycKwWYiIE9OiDgYUR9WatqEXDh8WOcFAEh6vi9+VI5ZrikvBeUroIMTUtiBFijkCFFaO4ItGIgMWLF1s59JtvvmmuCbEGgpMEO1O1LgCzGiGiaAvBwKQm8MmdMWrKSzSA/SlYBP6oBYrisBrCpmQBiwIh4vfAVaTlAOXsTIvjfFSapvM3iwMSjSzDjk0CbNQEELOgmxYLmw9fOrBA2JRFWpW7IilVGueU192wPEUDWNCIMJYXxVvEObAa0ukjyt+LoChWzPz58y3NS8C60Os6woqGHLuQYGVwl6KUmapOWvmnE5lnPwqBTvaPsFAxw5kjwhCiQq8zIKvCde7Spcu61oUESwmapgquCpsDEfsVK1aUOXpBJEbZkxSg2Q0LOt1IPIJBcI47KdvjSRX26dMnrZhIpog6e1IWXG/cNmalMJu2a9euKTcXEhujYUkRQBfwdAUDrcbCIDZC9gVXJFcEI9fgehMMHjJkiLmHjKBkbgrBaBE9Eo1ywO+0ReUiqVpqMNgeL8EoHUQaV5CNejReRkAIaBLzENEi0SgHKDwaNGiQNZRhwxXNcyQYyaFGhdQzm9MIYPbt29fNnTvXe1ZEhUQjYmhCM3ToUIvgs62dVK0IT79+/ezaqdlw9Eg0IgafnC3hF1xwgQ1AUjAvNYhz0Now7B4VkT4SjYhBKMhMlGcNRlygNkaiGz0SjYjBnMYfp8WdEPmIREMIEQoVd4mEUAuBC8W+GpEbUM/DcO3isIuXJk8tW7b0HgmPirtERqB8m+pLkTvQSJot/jNmzDAXl/051PuMGDHCsnFR3f9laQiRJ8ycOXNdU+nBgwfbDmvK6wms04+WsRip9FuRpSFETKGFIRk3duoCrRToFEeD6XR3WYdBoiFERCxbtsz6g9BHljYILPgwUEnMOWgTwBhOv0UDvWjZERxVVze5J0JEAB3IKH9nJCUDs2rWrGlNlmivwIJPBnts2OU7ZswYi2Wwf4kBUZ06dXLdunVLqz1DTrsn6BPdtRmp5x+oZphNR5yD4A8Xnt4WmGz4dkLkMix2xjSwyY6GS+yZGTlypBs3bpz3irKhhQL9aAlQE8eg/wqNmoYNG2ZrIUoiEw0WO81r/G3gTZo0sUE5nTt3NuEIAudgO/kNN9xgvTiZC9qzZ0/r/ZhOYxYhsg0ZD25y/ueUzzJf01woCAgDrQDImgBl9HQ2o1iQ8RZREploYB3QeYkFj4lGh2i2htN2ja3OQeAcN954o6k2/0eEaI/H5iXa1QuRq9CrNJ2YA1Y5QVDcGh8CocQ4oiYy0cCcGj16tOvVq5cVo+CD0e6fYUJBG+di1jGWkIuFUgPKPW3aNFNtsR6sN0YfMEcWf1qUL4ygYHOdPzoBAaFnadCiLJoO8Zn3N+iRfqU1APEN1lOURCIatORncDH5ZSK9/kYtNhtRmEKbuyBw0TDRfMHw4TG5JxuCuGKNUfQT1JIT2YOeKT169LAdzqRH6QHLTmfGUCaDvitkS+ghS+CT4dmcjybLuPtRb3yMJHsyZcoUGy3IhaKlXarg0tDhatKkSetEAsVGrQcMGKCSZw9EeuzYsTbjg2vCFnJ6aiaDvxEfTkSGDusIfN26db1nRbpg8ZFmJRlATIKbJTNeksHnngbIvM+HsQvchOkYny45OWFt+vTpVrFGB2hatqUKLk2tWrXswnNw4fhwEwzF1dHO0bVgvREk5kPKNWPhl/XhJHtFGz2i+fydGP7EXFXcQSbFFXqL/0xBdzauJdeUgqyg3dqwTBAYRjj4B+fwg6LpknMjDFBH0qLklRmAkw4sgMaNG7vevXvbB5wpZP3793ft2rWznHWhwzXG18UKIzPFhwuSpbR5HiuDQUL8vUhhc2fD9J0zZ473KiHWknXRIN5A4BKrwLcE+JByNyOAGbajNA1mmzZtarMw8Adbt26d1gCdOMF1pfdomzZtTKC5QzGpLdk1xkNlcFDxehcew1JhNogQxcm6aBCkYVETNaZABfgg+t2kFcDMDAgDrgVpbLZPU/RDuTIWQzLRIC5EvKl4VSGPYQIHqVYUhUXWRYOADy4FO/AIzo0aNcoq4zCjGfmX7vwQsdYtIcYzfPhwK01GlGlgjIXHoKFkokEWi8g+BXf0Z0A8cG3YPcnfTojiRJI94YOLK0KdBiAkbdu2tQ94OgUvYi0ELCdPnmzbpamH8d1ASpQnTpxo15lRCckYP3689Wsge8JOSkTD31Ep4kvY7Ik2rOU5BC5nzZplRVzEMUiGEVWnPoNAMfUa5PQ5KAQSoiTqp1FgECcijkEgk41MlBsTJyJehAtIcJR9C1FvahLxRZaGEAWOLA0hRFap8Nufq2VpCCEC4tz/AYC0sPORJ+sTAAAAAElFTkSuQmCC)
Figure shows a glowing mercury tube. The illuminances at point A, B and C are related as
![](data:image/png;base64,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)
A block rests on a rough inclined plane making an angle
of with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block (in kg) is : ![open parentheses text taken end text g equals 10 ms squared close parentheses](data:image/png;base64,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)
A block rests on a rough inclined plane making an angle
of with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block (in kg) is : ![open parentheses text taken end text g equals 10 ms squared close parentheses](data:image/png;base64,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)
In
then the triangle is.
In
then the triangle is.
Two masses
tied to a string are hanging over a light friction less pulley. What is the acceleration of the masses when they are free to move ? (g=9.8
)
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)
Two masses
tied to a string are hanging over a light friction less pulley. What is the acceleration of the masses when they are free to move ? (g=9.8
)
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)
A machine gun fires a bullet of mass 40 g with a velocity 1200 . The man holding it, can exert maximum force of 144 N on the gun. How many bullets can he fire per second at the most?
A machine gun fires a bullet of mass 40 g with a velocity 1200 . The man holding it, can exert maximum force of 144 N on the gun. How many bullets can he fire per second at the most?
One end of massless rope, which passes over a massless and frictionless pulley P is tied to a hook C while the other end is free. Maximum tension that the rope can bear is 840 N. With what value of maximum safe acceleration (in ) can a man of 60 kg climb on the rope
One end of massless rope, which passes over a massless and frictionless pulley P is tied to a hook C while the other end is free. Maximum tension that the rope can bear is 840 N. With what value of maximum safe acceleration (in ) can a man of 60 kg climb on the rope
Three identical blocks of masses m = 2 kg are drawn by a force F with an acceleration of 0.6 ms–2 on a frictionless surface, then what is the tension (in N) in the string between the blocks B and C
Three identical blocks of masses m = 2 kg are drawn by a force F with an acceleration of 0.6 ms–2 on a frictionless surface, then what is the tension (in N) in the string between the blocks B and C
When forces are acting on a particle of mass m such that and are mutually perpendicular, then the particle remains stationary. If the force is now removed then the acceleration of the particle is-
When forces are acting on a particle of mass m such that and are mutually perpendicular, then the particle remains stationary. If the force is now removed then the acceleration of the particle is-