Maths-
General
Easy
Question
An ellipse is drawn with major and minor axes of lengths 10 and 8 respectively. Using one focus as centre, a circle is drawn that is tangent to the ellipse, with no part of the circle being outside the ellipse. The radius of the circle is
- 2
The correct answer is: 2
![table row cell 2 a equals 10 rightwards double arrow a equals 5 semicolon 2 b equals 8 rightwards double arrow b equals 4 end cell row cell c to the power of 2 end exponent equals 1 minus fraction numerator 16 over denominator 25 end fraction equals fraction numerator 9 over denominator 25 end fraction rightwards double arrow c equals fraction numerator 3 over denominator 5 end fraction end cell end table](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOkAAAA7CAYAAACewa3HAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAjYkPj7AAAB3NJREFUeNrtnX9kZUcUx8cTsdYKUbVi1SMiYq0osWrFqrAqIiJCVOSPirCqqiJC/4ioWiGqqvaPsmqtqhVWxaqI/SciVv4IK6LWWqWqatVa8sda63qW1/n2ndd39+bOe3N/zZ2593w4f7wfyZszZ87MnHPnnitEOKNSfpHyUkpNyrGUeWEHg1LWqE0qeqT8IOWQ5Ba9VxTqbaQTUW37WkrFkF5npdyU8kqKJ+WBlAuGftuknn4mNe12in0pc1LO0euLUg7ovbz5Wcr1DortSpkKdMRuwZw0LlFsOyDlN4N63ZayLqVLSreUDZpks8a0nk1ggycJ7fkW1ZwUiTpQZ2k2DvK9JZNM3k4axbbTUjYN6uUFXldotc8a03o2wQ5vMW17eiHvoSO/lvLct32q5jhQsZX7KOT9MfosKisRtsqm+qJuwEHAV1JWSad/6Dt7Uvoysukr3wrf7M+/Y/6vKHYzrWcz7NhN255XaFsUZJtWrl7q1Hs0M8WJp+oRGqz63gltlYJ0k/NEBcb7izq1E6b6QrePNum70zFti/b/IeVLn07fdVh1ktgXffdFoF3fxhyvUexmWs9u2rlU03TSMxQbBBWeIwX9/CRlIseV9E2bv6kl6PA6xUuq5ILJvqiTLkj+7EhZDqxAUZxUZVvwO8Wsfnrod7NgmPSqUeyMVe1qQkfpZLc89ESs/XmaOyPMLPcVW8g9mu2CiYmqpU7qJUxq4DfvKj7Poy+QYBkRjWz3UylDKdoWg/q1wqmzGLxV6ts+305ohFa44QztZlrP4ZBdSyIn7ScjDig+D6atKxRXdHKuLLe7zxXb3TNttru6M/JGmxk5z74Q5Gj7Kdr2A5p4wrbGuxnotKVwxjFFO9Kym2k9D0P6PLaTYlb+UTSuXal4ERIMHxnKjLVLHI0rBnGcxJFubJNnX0TdKejYFtv3OyHvL9PKbbLtXoZ2M61nWpOyOE/xVVeH7z2jFarJWkxHSNNJZ2gABrkj4l2CWVHEezb1BbhEW8O0bIskzoIi4ZFF1vOJYlW/SLFpVnYzrWeUsdyWbc345oZoXOup+GKKHQsUw/ZlSbQuiq9G3ArGwWRfbNF2rEIyTg46o5E40rXtFiVUrtHrC/TeQkY6zZCjjvn0GiO9Ps3Qbqb1TM1JoyzHqzQzr/nivumMFerUpl5KGHgUK97SnFWTYqovZmlgIUl2Qr95OeR7YU6qa1u0fcr3O8cZ27WpF0KEGtlu38Bv5qFnKk6ahHcFY1NfwFEn2BQMYyfvS3msEX8yDJMTiK/OczcwDMMwDMMwDMMwDMMwDMMwDMMwDMMwDMMwjOXo1AYGOBSPw/GoAIAD5b9K+dASHdCOh6J1kwJuu+svsU1xR84O9QX6BAfyUYHyHR7ubqJTG/g6OeUgvUZNnXlyjLzBDfKPaRLBLWM4+4vSkyjRUtZjhrj9EbfT+at+4Gz0Ax7ubqNyUtzI/Mjidj9SrJq4lewbNutbvOQuKKaT4v5Wmwt1q4q5YVU9YrP+Tz/tLpgCOikM22dxu1ENYSTk/aoIr6xXNrDlX6C4lO/VLaiTehSLbtGgr9EW05aHYmFb+6doJI+apUwmRatqQpnt6ZclHuLFddI6DXjMwl3kBKM0M39mSdvhoHs0oUCQhR7glfQ/UJ4HJVYOhT3Z+NRnIszGB0Jd87XoTopkQ9gj/ZAtfGaxPs1q90yDc0XujwqtGEclddIdoS7WbPN2EtcKb7BvngpdWMECOikmqI9D3h+yfGZeF+Ye6usCwxSiFBbs5fdL6qTdpPuiaBUJw+MOUJD5mgXtxuMV/Bfu4Zg4QTVVYoeEvWZ9OQTsKpBc+6SoCvdRTJrlMTPdo3lZxt7tagOj3Ccq7eN5MW9oEFy1xD6YKPaoXYifN0WyhyYVAdhmW7QSaeifyaIqO0jKZn2dUOdoHsMwISsokiY9Bn+TnZRhAiAtjfOduJSATCUu2PfSZ3DQIcPtYSd1g5WIk3e7ccZ06DhcVlmnDu+mzp+MEKu1i+vSfI6p66T5bFMb0H1Uoc44K3I/JQYPa71p4WBm3JlY6uR8FcfGmROgU19YuOWopzR4kg68uJKns+TR5tv0P+5aMM5sslkq4Abhh4Y7iLe7bg0W3UG+0WYljTrOeLvrY4KCdxsHBlOcmNTWceYEuP/wKTspExMkfs45PM6c4ZiCfhydQtZtSehl69hJGdfHmTO8JxrH23CcDOdQFy2LfxgeZ0zJwWyO0pc471qjGX9ecwLJayJxsc22TPo8+TsIZvc5X2yFqoAH4nTRsTq32UknZQpKlbZkLhncxTazkzKJ8Bw0uMeDlPUvC1do++iSwV1sMzspE4tm4a7REIMjSYNkDe4MWhZ61wi5zfk6aZn1LyQ4W3pfNJ6rogLX+XBxHhUkcIF+iNtsPWXXvzD002CPUrIUjrHPbXaKsuvvLJhZUbvobIy/9bjNzuHxkHcLPCPknmhVAIzCJdF4Bgu32R3Krr+TbGvGKLiLAxnU5nNWxsnYM9xmaym7/oVB9+gY6reiqDLOnp7QSnaZ22w1uen/LxCYSKpBa+XDAAACD3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtdGFibGU+PG10cj48bXRkPjxtbj4yPC9tbj48bWk+YTwvbWk+PG1vPj08L21vPjxtbj4xMDwvbW4+PG1vPiYjeDIxRDI7PC9tbz48bWk+YTwvbWk+PG1vPj08L21vPjxtbj41PC9tbj48bW8+OzwvbW8+PG1uPjI8L21uPjxtaT5iPC9taT48bW8+PTwvbW8+PG1uPjg8L21uPjxtbz4mI3gyMUQyOzwvbW8+PG1pPmI8L21pPjxtbz49PC9tbz48bW4+NDwvbW4+PC9tdGQ+PC9tdHI+PG10cj48bXRkPjxtc3VwPjxtaT5jPC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz49PC9tbz48bW4+MTwvbW4+PG1vPi08L21vPjxtZnJhYz48bW4+MTY8L21uPjxtbj4yNTwvbW4+PC9tZnJhYz48bW8+PTwvbW8+PG1mcmFjPjxtbj45PC9tbj48bW4+MjU8L21uPjwvbWZyYWM+PG1vPiYjeDIxRDI7PC9tbz48bWk+YzwvbWk+PG1vPj08L21vPjxtZnJhYz48bW4+MzwvbW4+PG1uPjU8L21uPjwvbWZyYWM+PC9tdGQ+PC9tdHI+PC9tdGFibGU+PC9tYXRoPocB8D0AAAAASUVORK5CYII=)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/849958/1/1085081/Picture152.png)
Focus = (3, 0)
Let the circle touches the ellipse at P and Q. Consider a tangent (to both circle and ellipse) at P. Let F(one focus) be the centre of the circle and other focus be G. A ray from F to P must retrace its path (normal to the circle). But the reflection propety the ray FP must be reflected along PG. This is possible only if P, F and G are collinear. Thus P must be the end of the major axis. Hence r = a – ae = 5 – 3 = 2 alternately normal to an ellipse at P must pass through the centre (3, 0) of the circle
![table row cell fraction numerator a x over denominator cos invisible function application theta end fraction minus fraction numerator b y over denominator sin invisible function application theta end fraction equals a to the power of 2 end exponent minus b to the power of 2 end exponent rightwards double arrow fraction numerator 5 x over denominator cos invisible function application theta end fraction minus fraction numerator 4 y over denominator sin invisible function application theta end fraction equals 9 open parentheses theta not equal to 0 text or end text fraction numerator pi over denominator 2 end fraction close parentheses end cell row cell fraction numerator 15 over denominator cos invisible function application theta end fraction minus 0 equals 9 rightwards double arrow c o s invisible function application theta equals fraction numerator 15 over denominator 9 end fraction rightwards double arrow text end text text w end text text h end text text i end text text c end text text h end text text end text text i end text text s end text text end text text n end text text o end text text t end text text end text text p end text text o end text text s end text text s end text text i end text text b end text text l end text text e end text text end text rightwards double arrow theta equals 0 text end text text o end text text r end text text end text pi divided by 2 end cell row cell text end text text b end text text u end text text t end text text end text theta not equal to pi divided by 2 rightwards double arrow theta equals 0 end cell row cell text end text text H end text text e end text text n end text text c end text text e end text text end text P equals left parenthesis 50 right parenthesis text end text text i end text text. end text text e end text text. end text text end text text e end text text n end text text d end text text end text text o end text text f end text text end text text m end text text a end text text j end text text o end text text r end text text end text text a end text text x end text text i end text text s end text text end text right square bracket end cell end 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)
Related Questions to study
maths-
From a point P, perpendicular tangents PQ and PR are drawn to ellipse
Locus of circumcentre of triangle PQR is
From a point P, perpendicular tangents PQ and PR are drawn to ellipse
Locus of circumcentre of triangle PQR is
maths-General
maths-
The least integral value that contained is the range of the function f defined by
is ___
The least integral value that contained is the range of the function f defined by
is ___
maths-General
maths-
Let
then
Let
then
maths-General
maths-
If m is the slope of tangent to the curve
then
If m is the slope of tangent to the curve
then
maths-General
maths-
If
is equal to e7, then ![stack l i m with x greater-than or slanted equal to 0 below fraction numerator f open parentheses x close parentheses over denominator x to the power of 3 end exponent end fraction equals horizontal ellipsis horizontal ellipsis](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGwAAAArCAYAAACdO20ZAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAZpE86XgAAA4pJREFUeNrtW0FoFDEUDaUssoiwSClFSkGkiIdS8CAi4qWIyFJkL9KDh1IQKaV4E08eRCg9FCneehARWSgiUooIIksp0ssiIiKlIOJBRIQ99FCKFOr/9A/GmEySmYzuzPwHj+78ZDLT//cnPz9/hcgnpoFznvfM0X2MDNED7FdkI8CNhOO9ofsZGeASsEP8AOyVlD6acMzTwHVWbXigcb5KhjlFf0fJYGmwToZjBEQD2NTI54EzKceeTbD+MSy4A7ylkb8EntfIpwxGuEttMs4CX7OKw+EZcF/ihNS2DawY7nurBCiTwAeafhUahxEQm8BBjXzPEqQs0Ocxixf9ZBWHDeV3DG17lntfAS8A3wGPssH+Dc4AW4a2uCkRcZOMEbfX4ikxMHDNehjjQecMbSh/StPiRMz4HHQExiLwuqHNFNYfB64Aq8DDwHbMlDhD4zACRomXDW26jXMf8IVioDrwcdk2zjsUANhkoYGpqEMx7RvSGlUhAx/T9GtS5CijsKmpE8D3DrLQQG/5ZunDyV8Nrgh9aihL3Kf9l0va6IbwTy/Nx6yNuYcuNaTKout+ChS+k3dE60+NIrYOhdG3Lc/E6arBS3gyLJOXxcmWyWhtCqMxwz4E/AwcAK4Br5Icsxa74u+zrW7HvgO7AluahVyVbdF+pqb0w2ORJYN8gH0hPHSpIVUWXVcN/aoOY/p+k7NkrqFLDakyU/rIV85TYkapIVVmSh/5yhkZpYZQNmXpk0TOyCg1pMpM6SNfeVGhTpehr62pIVVmSh/5yrNUFh6z4LnYxaIbrEg4CfzCk2a+tigdVkM+gMctWIQzyarIz6J/jVWRHxwB3uPtRP6wW3YFNEV8CZkKPK7fJNZTPNenujcCVgm3y24wPGLBX5O4nF1hhdIaGRjZIllSuFT3RusXehaWdg8V1RBY6zAihcNx/ywq/4mDtz0XB4Wd8jd+JcU7+lT3Fh518bssYMHRg2zeti3+LNrpEemLOF2re0sBVAJWzy553DMM/BETXqtIWybtUt1bGixScFDxWM+wkmrc0cN6U3qYa3VvKTBGU+JHcVBuZssi4BqGxZo1jzUMP68mfD+f6t7CY5CiOVTENIXKrl4VGc8UJbbIqH30jCTHLL7VvYVGhSLEYen6ExlPB9mrbFNipFgs2MEk7GzC9/Op7mUYpkRU1iPLlMjoAjQomqyzKvIB9qr/iF9clhWKir+YNAAAAV10RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXVuZGVyPjxtcm93PjxtaT5sPC9taT48bWk+aTwvbWk+PG1pPm08L21pPjwvbXJvdz48bXJvdz48bWk+eDwvbWk+PG1vPiYjeDJBN0U7PC9tbz48bW4+MDwvbW4+PC9tcm93PjwvbXVuZGVyPjxtbz4mI3gyMDBBOzwvbW8+PG1mcmFjPjxtcm93PjxtaT5mPC9taT48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bWk+eDwvbWk+PC9tZmVuY2VkPjwvbXJvdz48bXN1cD48bWk+eDwvbWk+PG1uPjM8L21uPjwvbXN1cD48L21mcmFjPjxtbz49PC9tbz48bW8+JiN4MjAyNjs8L21vPjxtbz4mI3gyMDI2OzwvbW8+PC9tYXRoPoSKqLAAAAAASUVORK5CYII=)
If
is equal to e7, then ![stack l i m with x greater-than or slanted equal to 0 below fraction numerator f open parentheses x close parentheses over denominator x to the power of 3 end exponent end fraction equals horizontal ellipsis horizontal ellipsis](data:image/png;base64,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)
maths-General
maths-
Set of all values of x such that
is non-zero and finite number when n N
is
Set of all values of x such that
is non-zero and finite number when n N
is
maths-General
maths-
The period of the function
is
The period of the function
is
maths-General
maths-
Let
is a prime number and [x] = the greatest integer
The number of points at which f(x) is not differentiable is _______
Let
is a prime number and [x] = the greatest integer
The number of points at which f(x) is not differentiable is _______
maths-General
maths-
If the line
is one of the angle bisectors of the lines
and
then the value of k is
If the line
is one of the angle bisectors of the lines
and
then the value of k is
maths-General
physics-
A particle when projected in vertical plane moves along smooth surface with initial velocity 20m/s at an angle of 60°, so that its normal reaction on the surface remains zero throughout the motion. Then the slope of the tangent to the surface at height 5 m from the point of projection will be
![](data:image/png;base64,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)
A particle when projected in vertical plane moves along smooth surface with initial velocity 20m/s at an angle of 60°, so that its normal reaction on the surface remains zero throughout the motion. Then the slope of the tangent to the surface at height 5 m from the point of projection will be
![](data:image/png;base64,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)
physics-General
physics-
Consider a particle moving without friction on a rippled surface, as shown. Gravity acts down in the negative h direction. The elevation h(x) of the surface is given by h(x) = d cos(kx). If the particle starts at x = 0 with a speed v in the x direction, for what values of v will the particle stay on the surface at all times?
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)
Consider a particle moving without friction on a rippled surface, as shown. Gravity acts down in the negative h direction. The elevation h(x) of the surface is given by h(x) = d cos(kx). If the particle starts at x = 0 with a speed v in the x direction, for what values of v will the particle stay on the surface at all times?
![](data:image/png;base64,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)
physics-General
physics-
System shown in figure is released from rest. Pulley and spring is massless and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with ground is (Take force constant of spring ![open k equals 40 N divided by m blank a n d blank g equals 10 m divided by s to the power of 2 end exponent close parentheses](data:image/png;base64,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)
![](data:image/png;base64,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)
System shown in figure is released from rest. Pulley and spring is massless and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with ground is (Take force constant of spring ![open k equals 40 N divided by m blank a n d blank g equals 10 m divided by s to the power of 2 end exponent close parentheses](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOAAAAATCAYAAACJKwFWAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAABOVJREFUeNrtWmFklVEYPmbmmoxrZq5kJNmPzMhM9mNGJkkmkiSTkSRJYjKTZGSSTMYkkySu6Udmf+aayWTMZD8m989MkolrklzXWO/R8+k495zvnPPd77v3ts7Dy73v+c75zjnPec953/d8jHl4eMSJfUiJZIXkmJ8SD4/qo4HkJsm6n4ro6MYu5uG5j4qi8PsxjNLDEi9Irvhp8NxHRD/JsqTjRt1l28AvHKXVxDn40Cq0kEyTrEJmoNNhl2Q44tjaSLZqMP6k8KvOxnKcZJzkU8gzrnzHhTi4z8DYjkr6kyQfbBrgweNGlUk5RLIZYoA5kvOSseZC+r+pGazN2MawQA4CasGlCa9Jrodw7cp3nKiUe765zMMIVfgAQwzFEMnbKpPCd7gRDSkXSaYU+mcklzX9f0PyChPiMrYG7IBtB8QAa8GlLXQG6Mp3nMmTSrjnRrdgOKlvIx4MxQOSUfxuxEI+m+DA+4TdTUXKHMmgQj+AMl3/eflEyNhU4AS/tJibdiySHZJvwvykSZ6SFEh+kNw3EP4QbZTgknUo3ncP75uFO1kAkSovYgrudxFz89wwXo5mkkmS7471kjJAF77j5MPEfXBCbpPsof/iHHHj6zTUP2Vzkmexc6bwe8BiIk2iQxNcpI4QUgp4TlV3J6T/QeCrK4viImRB+hoIa0Tft7AD8sD7EvRHsKDbNW3NY9GkYYyqvmVhbLMI7Plzh9Fus2TMSyTX8LsF/dw3jLcRfR7Fby53scCGEuDbxgBd+I6TDxP3Y0jQNDnMi2oMP0wTkyc5QfKepDfhXZAfx7cMpOyF1C9p+n9Y2CFPC2WfhTIZNunnPHawtKT/CnJU+oxmt81KOpWnkUe8pFqkrcL/cc2JlQ8Zb1BvQlMvU6MT0IXvuPiw4X5FWktRUTL5wdzN+QgjTBJdikG7GmBR0/8AHVjYqjIZpvRzUL/ZUa/CEtwREcuSC8rr/9ScWnK7X+CC2r4/wDfJkMPeWw8GWEyID5urBx6brkvJodgNsBeLw8YfrtQlWWXln+uont3RHPsphUsS9F/EIhanqiyATfpZV99Vz1j51YBq0evqn5L03az8zsn0fsb0aXFTvaRdUFu+4+LD5eohgzlbUmx4NjC6oJcRb3A8IbmR8A5oQyIPvM8o6g8qgnKx/wGG4capykT/3pR+1tV31TMkPORE1HrEdi+wP6l9l/dXUq8aSRgbvuPiw/XqIYW8xdUIYzYmYaakmGMRi6Na2NcslBcK/SwrT0vz/o8odp2cYmzi6WOTftbVd9UHsUhKisXmLMai0g8p4knG/t636cBdqbeaeiM1NEBbvuPgI+rVw0sW7WsZnu+YDHvgnZQISMNVzNTQAIOY6Q7inybsWssW/Rd9/A1Nma27rWvbVc/xiP25+2xA3MfvLRcitstjnU24ooFrOQ8jD7s+aoFL1y24snOo119Drm35joMPl1ArQA/muzXCmI0X8QVpZ2ZIxuQU+mqSksZEFRE/zWh88IKmn31oOxVlUgxtu+pF1yeL0y+Ib4YittuOBVZEAm3A4v3BKbiNxMAa3LzvLNlP12xiRhu+4+DDlvtd9HMPm0NnhHFbf4rmURvUw9c3J1j9fjnzr8PpY2yPgw++i08L4UUPFkmnn5rYMWmIxz3+QwSfrv2Em7fAkr/79QB+A9KGp60QKP+TAAABQ3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZmVuY2VkIG9wZW49IiIgc2VwYXJhdG9ycz0ifCI+PG1yb3c+PG1pPms8L21pPjxtbz49PC9tbz48bW4+NDA8L21uPjxtaT5OPC9taT48bW8+LzwvbW8+PG1pPm08L21pPjxtaT4mI3hBMDs8L21pPjxtaT5hPC9taT48bWk+bjwvbWk+PG1pPmQ8L21pPjxtaT4mI3hBMDs8L21pPjxtaT5nPC9taT48bW8+PTwvbW8+PG1uPjEwPC9tbj48bWk+bTwvbWk+PG1vPi88L21vPjxtc3VwPjxtaT5zPC9taT48bW4+MjwvbW4+PC9tc3VwPjwvbXJvdz48L21mZW5jZWQ+PC9tYXRoPhGlFO4AAAAASUVORK5CYII=)
![](data:image/png;base64,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)
physics-General
physics-
A smooth track in the form of a quarter circle of radius 6 m lies in the vertical plane. A particle moves from
under the action of forces
is always toward
and is always 20 N in magnitude. Force
always acts horizontally and is always 30 N in magnitude. Force
always acts tangentially to the track and is of magnitude 15 N. Select the correct alternative(s)
![](data:image/png;base64,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)
A smooth track in the form of a quarter circle of radius 6 m lies in the vertical plane. A particle moves from
under the action of forces
is always toward
and is always 20 N in magnitude. Force
always acts horizontally and is always 30 N in magnitude. Force
always acts tangentially to the track and is of magnitude 15 N. Select the correct alternative(s)
![](data:image/png;base64,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)
physics-General
physics-
Ball I is thrown towards a tower at an angle of 60° with the horizontal with unknown speed (u). At the same moment ball II is released from the top of tower as shown. Balls collide after two seconds and at the moment of collision, velocity of ball I is horizontal. Find
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)
Ball I is thrown towards a tower at an angle of 60° with the horizontal with unknown speed (u). At the same moment ball II is released from the top of tower as shown. Balls collide after two seconds and at the moment of collision, velocity of ball I is horizontal. Find
![](data:image/png;base64,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)
physics-General
physics-
A ball of mass ‘m’ is rotating in a circle of radius ‘r’ with speed v inside a smooth cone as shown in figure. Let N be the normal reaction on the ball by the cone, then choose the wrong option.
![](data:image/png;base64,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)
A ball of mass ‘m’ is rotating in a circle of radius ‘r’ with speed v inside a smooth cone as shown in figure. Let N be the normal reaction on the ball by the cone, then choose the wrong option.
![](data:image/png;base64,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)
physics-General