Physics-
General
Easy
Question
A 0.098 kg block slides down a frictionless track as shown. The vertical component of the velocity of block at
is
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/904353/1/923693/Picture33.png)
The correct answer is: ![square root of g](data:image/png;base64,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)
or ![v equals square root of 4 g equals 2 square root of g](data:image/png;base64,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)
Vertical component at ![A equals 2 square root of g sin invisible function application 30 degree equals square root of g](data:image/png;base64,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)
Related Questions to study
physics-
Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are
respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at
,these two particles will again reach The point ![A ?](data:image/png;base64,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)
![](data:image/png;base64,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)
Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are
respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at
,these two particles will again reach The point ![A ?](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General
physics-
The trajectory of a particle moving in vast maidan is as shown in the figure. The coordinates of a position
are
The coordinates of another point at which the instantaneous velocity is same as the average velocity between the points are
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486211/1/923664/Picture20.png)
The trajectory of a particle moving in vast maidan is as shown in the figure. The coordinates of a position
are
The coordinates of another point at which the instantaneous velocity is same as the average velocity between the points are
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486211/1/923664/Picture20.png)
physics-General
physics-
The potential energy of a particle varies with distance
as shown in the graph.
The force acting on the particle is zero at
![](data:image/png;base64,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)
The potential energy of a particle varies with distance
as shown in the graph.
The force acting on the particle is zero at
![](data:image/png;base64,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)
physics-General
physics-
A
mass moves along
-axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from
to ![x equals 8 blank c m](data:image/png;base64,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)
![](data:image/png;base64,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)
A
mass moves along
-axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from
to ![x equals 8 blank c m](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEIAAAANCAYAAAAdWrhRAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAcRJREFUeNrllkFERFEUhp+RkYxhJGNkRFq1mE2SjGRokdEikcwykVZpEWnVIjGSFmmXtEgimUWLRJK0iozRIom0SJJokWSMqP/wx3PdO3On6VW8w8d757zz3nnn3v/e6zh/Zw1gBbyCIjgAzY4PbR0sgDoQBFlw5sdGFJX7ACj9h8LGOCqqzTP20yaSCCmNuLPMlbxFcM/m5UCEsTkwA6KU3iN4AGnG5bll8AxewKzuA3m+4MtGwWqZgj4sMJkUOem67wZLlk3IU1ZhymoaDDC+w2acgwyl1wJuQQycgBH645yZUfUj/eyWWB848nAGJjiaJRYno9ZjkZdlE012zbojil9mz5rBH9O96BD0ggJo9KgJMkJbLCBIXwe4YYNMJvJ50vyMO/7GHakav9amOEoJix/6rjRyhvenwHGZ73WC0zLxLkN+tX4nCXYpj8wv7hi2sTSbaDKpeaNWfyvY4/QJcbHxShqXoE3jb+daYTKRz1WFBXi8Fn8T2Fd+XFbhTY8aMcRmpKjTAK9ljZiokFtwHcTClHLSJbm0QYoV/UE6dMfbbe4kXtgwt8ES5SA7x6BFXpzPvoML5YwjZ4N6TU61fv/aJxNyckLX091sAAAAgHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT54PC9taT48bW8+PTwvbW8+PG1uPjg8L21uPjxtaT4mI3hBMDs8L21pPjxtaT5jPC9taT48bWk+bTwvbWk+PC9tYXRoPsQG1+QAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
physics-General
physics-
A mass
slips along the wall of a semispherical surface of radius
. The velocity at the bottom of the surface is
![](data:image/png;base64,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)
A mass
slips along the wall of a semispherical surface of radius
. The velocity at the bottom of the surface is
![](data:image/png;base64,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)
physics-General
physics-
Three forces of magnitudes 6N, 6N and
N at a corner of a cube along three sides as shown in figure. Resultant of these forces is
![](data:image/png;base64,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)
Three forces of magnitudes 6N, 6N and
N at a corner of a cube along three sides as shown in figure. Resultant of these forces is
![](data:image/png;base64,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)
physics-General
physics-
A man standing on a hill top projects a stone horizontally with speed
as shown in figure. Taking the coordinate system as given in the figure. The coordinates of the point where the stone will hit the hill surface![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486231/1/923529/Picture18.png)
A man standing on a hill top projects a stone horizontally with speed
as shown in figure. Taking the coordinate system as given in the figure. The coordinates of the point where the stone will hit the hill surface![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486231/1/923529/Picture18.png)
physics-General
physics-
A particle is acted upon by a force
which varies with position
as shown in the figure. If the particle at
has kinetic energy of 25 J, then the kinetic energy of the particle at
is
![](data:image/png;base64,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)
A particle is acted upon by a force
which varies with position
as shown in the figure. If the particle at
has kinetic energy of 25 J, then the kinetic energy of the particle at
is
![](data:image/png;base64,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)
physics-General
physics-
A bob of mass
accelerates uniformly from rest to
in time
. As a function of
, the instantaneous power delivered to the body is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUgAAABkCAMAAADT01n4AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAL6UExURf////39/fX19fHx8fr6+u7u7pGRkWFhYWVlZcPDw+Pj40RERAAAAJmZmebm5kdHR/f391NTU5aWlunp6ba2tj09PRERETc3N7m5ufv7+9TU1MvLy8nJycHBwdzc3P7+/qqqqi4uLhAQEEZGRsTExPDw8M3NzVBQUDIyMjExMY2NjYuLi3BwcNLS0mBgYENDQ6mpqZKSkl1dXcLCwmhoaAoKCktLS8zMzJSUlAYGBh4eHjo6OhcXF19fX7y8vJ6engkJCR8fH2dnZ8rKyu3t7cDAwAsLCwcHBwgICAwMDOvr65iYmDw8PPLy8uzs7KSkpCMjIw4ODk5OTtHR0fb29q+vr0lJSRQUFFdXV4iIiB0dHV5eXru7u729vTU1NU9PT39/f0pKSk1NTUJCQj8/P9/f3wQEBBYWFkFBQSUlJYODgycnJw0NDZOTk4KCglpaWtnZ2eTk5AICAuDg4FFRUWRkZMXFxYmJifn5+QMDA8/Pz4eHh/j4+IaGhm1tbbi4uOHh4SwsLGZmZpWVlUBAQCIiIoqKioyMjOXl5fT09KioqC8vL7S0tPz8/CgoKFtbWzk5OQUFBdDQ0PPz89XV1ZubmxgYGBUVFdPT09jY2Dg4OA8PD5CQkOfn5zAwMKKiourq6pycnHNzc9ra2gEBAUhISFJSUu/v70xMTH19fVhYWHt7e1RUVL6+vt7e3hsbGxoaGiAgII+PjyYmJpqamoWFhcbGxoCAgHJycm9vb25ubmlpaaGhoc7Ozrq6uhkZGTMzM6urq46OjkVFRdfX19vb26CgoOjo6GNjYxISEqampoSEhN3d3cjIyHR0dCEhIXV1dYGBgWxsbFZWVjQ0NHp6etbW1mJiYn5+fmtra7W1tRwcHJeXl3l5eS0tLT4+PikpKbCwsCsrKxMTEzY2Njs7O+Li4nx8fMfHx7KysiQkJKenp66urqysrLOzs2pqalVVVSoqKnd3d1xcXKOjo3Z2dp2dnXFxcb+/v1lZWa2trZ+fn3h4eAAAANB93R8AAAD+dFJOU/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////8A2NkMcQAAAAlwSFlzAAAXEQAAFxEByibzPwAACVlJREFUeF7tW1uyqyoUzA9f6i/fzMKxWMVorGJeDMDBWI7gdi/AmIdCzM7OqX3p5GSDKI9mvQDPpaKioqKioqKioqKioqKioqKioqKioqKi4q9Cxb8Vb0EN42xjuuINKN+2XUxXvAHVVCJ/BpXIH8FkG+3tZep7O8VLFWdgnG561TfOuyqX72Bo2/EyzW3bNiZeqjiDrm3nnjzOfbxScQog0nn9t3m0XRneogCqDbjxDU+jTOzIMb4W9fcNBCUP3c6TOr/K66SRxp6tQSllnHTkEVpvv82XZN4gviuDnufhNJNQbVYxnpUXO897PN5BN9+RyQUK18x5CN/+pGaqfuQIQcUSr7wKmQgX+3KDR4Ua4jO/Cxgv6Gz+05PJ5iSRE0c7ks2zg6SN1d2mP+mjGAug9vX7RSLHmDyGBQ1niew9tLq/oIZz0bgaMI1ueN76rbP00JudGz+LYiIvBkSetJETlBqWa3AIf85UMQk9MXMMxqr+G/6GRJaNzejzqg2JBJGTOelU+Xyho4PUf4/ImMyAi5OTRKpuEHVTw3LK8ZPIsSh0UiKRX1Lt+eMS+S4m8XTlRP7zEnnWRr4L2shXiPySRH7eRr4Lkcgiu/JdiSwjssBGqklCu5BhGl9Jp6AvpAOkAGA+04P/m0SqZW6AIA9G0o0s2NQS0gtbsnODojmt5BAjzqFgH8FGltDzJ2zkNMjCoh1NZ8y6hp+RjgWt61B0LWDOILhksG0ir09BiWzMPy+Rd15bCVIiXCNyEqkSXa0mJBF+QkYQCwRyW8xr7Q/CG0hkaRz570hkP874sNsDEpslXUYi1SLbM8vCX8ECgVtW3jYFre8MA+dbHLw/QImcuxImPyaRKndod2cjVR/GqzsrW4jerM8fS6TotW/maZoDd2ET18bNL+RSQat5/jWNsQQPNdwXwjTtyuRjHNlba+z2X+zZx2xk5zPbBPdEXkcb+VjPqo4lkqLnDN2vHHGlWm2sjuYjFuA2FqWcNnDamCRgd/n44LXV6NBB7fgb/sZhfkAi7TLi43P7LfdEcu7dIg5hHOgI1r2CY4nk3lBsCjLdLK6RRWEf5U72IXHPDAPgWDBxn4Zw4tYNc1yPP8VjHBln4Yq40VkgkXYBL4Uy2wNpwhdm9oHBbYiUAcGug17NjqOSdSIYR24oJxRrWJsLY1E9XwWADMk2BRWesj1TbdGWYUGHmimD3qMosteBcceCZwhExgygLC5oz9M0/Hrudsb5FiKPAyWMA31ln/vD+wCew7MRAZLe7X5424ZIwzxECUI1giF2ayXyyTZahyrmXo7917FYr72hMpIhOiBvUZscAAiRoMCBcosC02PedLAdciTDgme4t5FWNoon2nM0v5nFEtUWIrWM/nhnTnVs9gVsvDZ65hZ0A0OWRtCttTE4H7cMNxDtHNl3/g2iRb4xl751vRiKxlz6Wbth6nn7oKjSEC4aCsV31JI+c88S8eTAJh7+SRmnNgBciC/DX3Re1ChJpEFvHIzSPjbs+GGIrT+DuoYcZdgoLFRaciAUU8zzhauzCQ5hDzqdWJPISfbEoahxIiYPP8Ln6RNCG/BCEByIWiISbMeqdiDOPiC0gZEKkRIZrLKc4oRCNAc7zbR7r2AjkWGKE5HQ0uYa/oQT1T2s4hJ8EoikyUNPOPrJQ4AwegmmQhu4jUReJVIOX46wjcRkLvoRPaJws3RVnOTeSuEPZHJaxnGcY7+aGWnknwHXMeCNjcQg0UPFZRyIpOzEAgBD16Guu69gVbtAJBnynYpEUsVtL8qcao0SidtWkbdS0V3l8hVhXbui5PgIRDqYXjwtHUu1kF3d3D1/88WIExzyx+8Rc20H78n1V4dMXPbd44IPtWMlkjlOMSZVY4oDrQnINdzAefiGuhKiamOQNjkrZWkxyXAkMkhktADXgYSKnnwp39euhHexpA2JncKcBKTwBw891BK/aJ/g6nSRS1n0xpiRhByBirb2EGEnB4ueuQEiJtTFMmFoQ+suVonkIAORpoHTVmSYz3N6thJ5JXIXEt2ucaT4cDxMIqkIqGrtZmn4w20Sc7UVedjcuw1biYTyYRkslDlew9zJ0ANgIze5XQTBC0RyWFB61ANDAW8CZccfITLctvHaRwhxZGqcOT+IanOybs6JC8IfO3MfLyNfj8iJLhVt7SGGxeWbdVr6Auo2Mhh0Ngve1ied5bDmKSizguvRRpwzWqREhttWG7kPdGxLFojkpkogUtHlrGuZpNpHgH2iCflhhEEG0Mlg9JfJdGE53HWbfQQqekHzIFLDqMuSRVRSz3RoLILoeAxUL2iEt4kXKSLyViJRHx+CAnGyGDne2khR+J/BZMN2SPq7DxC5lboDHxaMXxay6uBouAUhu7agzFGCZJDMsY0UNhYddItErjZSLV621yeoKB/uZ7++Lsg2ZElxBC5rBVPudQW1OIlep9FdA+rn2EokHjw4PaGTKCBSjCAwyk5QCD7Dfg+DIclxHClslNtyuJXISzrkSQc/2wMg1Jo5t8AEJGM2ZN9cQ5dp3hfNV24OsbWRxyiUyLQzE6ZHcTOi1aETVEKoYXw1h07iaDd3g1sbeQQSOWcOJSYfWOFqNSNmnHsQSRnKkXQTRx6i0EaiSgesGwID0mn52DebAuR82czcS+QBxHxknA0tN/U1xLrHAJHoL+1fvLCLD0jkdLNFJbnUApIb94VcTGVwayMPQSIzzoYBvRi+MiI7BEwFR2/lRBZL5M/jVYk8ppy1QaXton3OLYlE2qYktPiARP48XrORWdVG5IkogiOPV3ZBG+nAe1ZyA5ExmcGfkUge8GFlhJHDj2QAIoHNVuguUF1RD78vkUU2skQiodXcTJh1OmTaR4zYSnSWXjsmMyiNIz+AQORPSaTIRIslakHo1cvmfAlD5aq93WT5ZbxoI7NLRAyFt5VUmDZysoBElv03Ip40fY1IykU2khPQO2R9MSUynPpk0fu4LssBEtl6OHfce/iVNwe+ReSFniHYlbU/Oz+QyCyPgcilaAdIdUM+9CGwjARB8jKB/OwlyOO6n//7gIF26Mjapb0fvgiTV0TUpvN0v4jyQ8cS4/wpWFrJMuS2aQDb+MLg+RVMMH4l+Or/EJZ3K4pQYvFV/iWLM5iWInxPrwUmdiOHEg9bUVFRUVFRUVFRUVFRUVFRUVFRUVFRUVFRUVFRUfEFXC7/AW7M5yvmI3IjAAAAAElFTkSuQmCC)
A bob of mass
accelerates uniformly from rest to
in time
. As a function of
, the instantaneous power delivered to the body is
![](data:image/png;base64,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)
physics-General
physics-
An aeroplane is flying in a horizontal direction with a velocity
at a height of 1960 m. when it is vertically above the point
on the ground, a body is dropped from it. The body strikes the ground at point
. Calculate the distance ![A B](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486223/1/923498/Picture17.png)
An aeroplane is flying in a horizontal direction with a velocity
at a height of 1960 m. when it is vertically above the point
on the ground, a body is dropped from it. The body strikes the ground at point
. Calculate the distance ![A B](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486223/1/923498/Picture17.png)
physics-General
Maths-
If the equation
represents an ellipse then
If the equation
represents an ellipse then
Maths-General
physics-
A particle of mass m moving with horizontal speed
as shown in figure. If
than for one dimensional elastic collision, the speed of lighter particle after collision will be
![](data:image/png;base64,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)
A particle of mass m moving with horizontal speed
as shown in figure. If
than for one dimensional elastic collision, the speed of lighter particle after collision will be
![](data:image/png;base64,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)
physics-General
Physics-
A particle of mass
attracted with a string of length
is just revolving on the vertical circle without slacking of the string. If
and
are speed at position
and
then
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/904329/1/923462/Picture16.png)
A particle of mass
attracted with a string of length
is just revolving on the vertical circle without slacking of the string. If
and
are speed at position
and
then
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/904329/1/923462/Picture16.png)
Physics-General
physics-
A simple pendulum is released from
as shown. If
and
represent the mass of the bob and length of the pendulum, the gain in kinetic energy at
is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKsAAACKCAYAAADVGLqKAAAYKUlEQVR4nO2de3BUZ/nHv+fsOXu/5042hKVEbqkFBrACpUiiDKLcUqzOQGlrpVVj6WBVCoLTUnUQm6pltEWHGRipFBR6IUGbhkwZhZQhjUJowqUhhdw25LrJXs6e2+8P5pxfliRlT2BJNnk/M2fIZLO7zyZfnvO8z/O8z0vJsiyDQEgA6OE2gECIFSJWQsJAxEpIGIhYCQkDESshYSBiJSQMzHAbQBi5yLKMSCSC9vZ2+Hw+0DQNnU4HABAEAZFIBDqdDqmpqUhNTYVerwdFUXGzhyJ5VsJAyLKMUCiE1tZWAIDRaIROp4MsyxAEATzPIxwOg+M4iKIIu92O9PR0mM3muAmWeFZCP2RZhiiKaGlpgcFgQFJSkipUURTB87zqVRmGQSgUQkdHBwRBgNfrBcuynytYWZaHJGgiVkI/JEnCjRs3wDAMUlNTodPpQFFUlMhkWYZyU5YkCZIkobe3Fz6fDxkZGWCYgaUliiIikQgMBgNoWtuSiSywCFEot/+Ojg44nU5VqAoURYGmaTAMo14sy4JlWdA0jc7OTkQiEQwUXfI8j5qaGrzxxhtqeKEFIlZCFKIoorOzEzabDSzLRj1GUVTUpSy4FNHqdDqEw2F0dXVBkqSo58qyDI7jcPToUfzmN7/BpUuX+v3M7SBiJUTB8zw4joPBYOj32K3eciDh0jStxq+3PrehoQH19fVYvnw5Lly4gJ6eHk22xRyzSpKE7u7uQV08YXQgCAI4joPVaoUsy5AkKSoMUGLVvjErEC3cUCgEURSjniOKIo4fP441a9agtbUV//znP5GXlweHwxGzbTGLVRRFFBUVoa6uDjRNaw6OCYmB1+tFfn4+HA4HBEFQ/9aKYJXFlCRJ/QTb9+u+nlUURfh8PvT29iI7Oxvjxo3Dvn37cObMGeTk5MScGdAk1oMHD8LpdGLx4sWw2WyDrvgIiYvL5QJN02ouVbm9980CiKIYJdq+4h2IcDiMs2fPwmg04vz582BZFqFQCG+++SbWrFmjLs5uR8xqo2kaHo8HOp0O48aNw+rVq2Gz2WJ9OiFB4DgOra2taoWKpul+KStJkiCKonrd6mkpilIXZ7Iso7e3F5cvX4bVaoUgCBAEAQsXLsTJkydRWVmJmTNnwmQy3da2mMXKMAyKiopQUVGBAwcOYMWKFbDZbGr5jTA6CIfD8Pv9iEQiYBgGNE1DkqQoz6eIUxHercK1Wq3qz4uiiMbGRvA8j0cffRRutxuSJOGhhx5CS0sL3n77beTk5MSUd4058KQoCrm5uVi+fDlmzJiBl19+GT6fb4i/EsJIhWVZmEwmhMNh9YpEIohEIuB5HjzPqyGCIta+XwNAUlISGIaBKIr4+OOPUVRUhObmZoTDYfV9WltbIUkSSktLceTIEfj9/tvapmmV1NPTA7PZjKeffhqNjY0oLi5GMBiMWvkREhuaplWxRSIRtf6vXJFIBBzHRQlXuSRJgtlshsPhiPKs+fn5+OIXv6iGEhRFQZIkLFq0CE888QSsVmtMd+iYG1lEUcS2bdvwxBNPwOv14tChQzh48CC2bduG+++/H0aj8Q5+RYSRhCRJ6OzsxLVr10BRFAwGgxoSKELr2yegiJWmaWRmZiIlJSUu4WHMnlWWZZw/fx5+vx80TWPJkiWYP38+3njjDfT09JDc6yiCoig4nU4kJSVBkiSEQiGEQqGosKCvp+V5HpIkwel0Ijk5OW5pTU0x64oVK5CWlgaapuF0OpGfn4+mpiaUlpZqrkYQRi4URal9qikpKaAoCpFIJEqwilBFUQTLskhLS4PH4wHDMHFrEbyjftaenh6UlpbiD3/4A7Zu3Yr8/Py4Nt8S7j2CIKCnpwc+nw9dXV39Hnc6nUhNTYXD4Yh7ZkiTWJUfVQQpCALC4TC2bNkCjuOwY8cOuFyufg0QhMRFyatKkqT2DSi5VJPJpPYD9K1yxYuYwwBJklBWVob29nb1ewzDwGw249lnn0U4HMbhw4cRCARI/DqKUEIClmVhNpvhdDrVy2g0gmXZfm2E8SJmsYqiiFdeeQWXL1+OfgGaxoQJE1BQUID9+/ejoaFBc+sXIXFQOqyGI9yLWaw0TcPhcMBisfR7TKfTYf78+Vi4cCG2bduGlpaWu2okgQBozAa89NJL8Hq9Az5mtVrx/e9/H5Ik4cCBA+jt7SXFAsJdRZNn/cIXvjBo84rBYMCECRPw+OOP4/3330dlZSUikchdM5RA0LTA8vv9CAQCAz4uiiI4jkN7ezuSk5Px2muvob29ncSvhLuGpgXW5s2b8emnn0IQBLUdTBRF9PT0oLGxER9++CEkScLGjRvB8zyKi4tjalAgEGIhphZBZZvt6dOn4fV61coGAHR1daG4uBiXL1/G1KlTsWbNGhgMBmzcuBE7duyA2+3GI488QooFhDsmpqKAMoVj7969EEURtbW16OjoAADY7XYsWLAACxcuhN1uVydycByHoqIi1NTU4Fe/+hUyMjKg1+vj/oEIo5eYK1jK3KO+jQuyLIOmaZjNZuj1+n7lts8++ww7duxATk4OnnrqKbjdbuJhCUNGU+pKr9fDarXC5XLB7XYjKSkJLpdLnYN0K5mZmVi3bh3ee+89VFdXk1QW4Y7QtMA6dOgQmpqa1CrG7WrCOp0ODzzwAJYuXYrf/va3uHbtGskOEIaMpn7Wffv2oampKeYXpygKFosFTz/9NGw2G/bs2YOenh7iYQlDQlOX7Lhx4wac1PF5sCyLpKQkfPe738WFCxdw6tQpcByn6TUIBEDDAkuZLGc2m4e0BbuzsxMlJSV46623UFRUBK/XS3bGEjShqdyampoKq9U6pDdyOp2YP38+rFYrjh49iu7ubtJKSNCEpjCgt7d3yAKjKAoZGRn40Y9+hNLSUrz99tskdiVoQlM24Pnnn+/Xz6oFlmUxc+ZMFBQU4J133sGlS5dI/EqIGU3ZgKampjvaGEjTNIxGI5YtWwaPx4PDhw+ju7ubpLMIMaEpZn3qqaeQnZ19x2+alpaGJ598EidPnkRFRYXaGEMgfB6aKlhLly6Fy+W64zdlWRY5OTlYtWoV/vKXv+DSpUskfiXcFk0LrDv1gEpDDMdxYFkWjz/+OFJSUvDKK6/A7/cTwRI+F03N13v37sX169eH/GY8z6Ourg7FxcXqnM4NGzagq6sLH3zwAYLB4JBfmzD60bTAKikpQVtbm/o9ZS+5MurwVvpOlpMkCe3t7aioqIDRaERJSQmqqqqQnZ2N9evXY//+/aivrwfP8yR+JQyIpjDA4/GoQ19FUYTf70dNTQ1Onz4Nn88HURTVW31rayv++9//4pNPPkFbWxsikQjq6upgNBoxZ84c5OXl4aOPPoJer8eDDz6IrKwsvPnmmyQ7QBiUmMWq0+mwc+dOTJ48GbIsw+/34+zZs2htbUVJSQl27dqFjo4OSJKEhoYG7N69GzU1Nfj444/x2muvoaWlBX6/H7IsQ6/XIyMjA2azGbIsw+1245lnnsH58+dx4MCBfid9EAiAxmyAy+VSu/17e3sxZcoUzJs3DytWrAAABINBhEIhVFVVgWVZfPWrX0VeXh5aWlpw7tw5MAyDiooK1NfXo7GxEW63GyaTCSzLYtq0aVi3bh2Ki4tRXV0dNXiWQAA0xqwtLS3gOA4URcHj8SAtLQ3BYBAXL14ETdNITk5GMBhEVVUVvF4vLBYLrFYrJk6ciJqaGng8HnAch9///vcoKSnBokWLYDAY1Bn0Dz/8MObMmYO///3vqpcmEBQ0lVt//OMfo7a2FsBNT9vc3Izdu3fjhRdeULescByHYDCI9PR0dWiX1WpFV1cXkpOT8ctf/hIvvvgitm7dqp4MouB2u7F27VpUV1ejrKyMnLlFiELT2UC3Nk7b7Xa1UHDs2DE8/PDDSE9PBwB1B4FyATcHuTmdzkELC3q9HllZWSgoKMA//vEPTJ8+Hbm5uWSjIQGAxnJrYWEhPB4PgJthgcPhwNy5c/Gd73wHixYtQn19PWRZhtFoRG9vrzoqUSkCxLJZ0GKxYO3atcjKysLWrVvh9/tJOEAAoHGBtXjxYrjdbgA3j6BRkvjKlGSHwwGXy4WcnBycP38e4XAYgUAAlZWVmDt3rrpN+3bvo9Pp8Mwzz8Bms6m9rwSCpjxr3wLAyZMnsWvXLnz44YeoqKgARVGYNWsWrFYrvvzlL6O5uRn/+9//UFZWhoyMDMycOTPmEwkpikJWVhY2bNiAd999F5cvXybFAoK2cuuePXvQ2toKWZYxbtw48DyPd999FzzPo6CgQN2jlZ2djR/+8Ic4ffo0/H4/nn/+efUsglix2+2YNWsWJk+ejL179w54LDhhbBHzHixBEPCNb3wDL774IubOnQuO49TT5QwGgzoBGYB6XKIyRdBoNA5pAK3SS7B9+3ZMnz4dmzZtGvK2GkLioylmnTVrFpKSkkBRFIxGI6xWKxwOR78hFzRNg2VZWCwWWCyWIY/xVloJ169fj3/96184c+YMQqGQ5tchjA40HYCh3Ibv9fHt7e3t2LdvH+rq6rBp0yZ4vV4yhmgMokl1yiSWe43dbkdBQQFaW1tx/PhxhEIhEr+OQTQtsM6ePTvgWUjxhmVZpKSk4NFHH8WJEydw9uxZMlV7DKKp3LplyxbU1NTE055BMZvNWLVqFaZMmYJNmzaR7MAYRNM9XTlwdrhQNi1OnjwZf/3rX6MawQmjH03l1p/85CdquXW4SE1NRWFhIf7zn/+gurqaFAvGEHd0dutw4ff78eqrr+LixYvYvXs37Hb7sHp8wr1Bc7l1JGjbbDZj3bp1MBqN+PWvf31HY40IiYOmbMDu3bvR3NwcT3tigmEYTJw4EWvXrsWJEydw8uRJUiwYA2jKBhw7dgxXr16Npz2amDNnDl544QUcOXJkRNlFiA+aNgzm5eUhKysrnvZowmQyYeHChQCAY8eOIRgMkkEZoxhNvQGFhYXIyMiIpz2aYBgGdrsd3/rWt1BZWYmysjIylXAUo0msdrsdLMvG0x7NGI1GLF26FLNnz8azzz6LGzdukMXWKEVTzFpeXj4ij2enKAqPPfYYFi9ejD//+c9obGwcbpMIcUBTNqCoqAgNDQ3xtGfIuFwu/PSnP0VtbS3OnDkzYtJshLuHpjxrKBQasQ0kBoMBWVlZmDdvHvbv349AIEAWW6MMTae11NbWIisra0intdwLBEFAU1MTioqKwHEcXnrpJSQnJ5Pe11GCpt6AadOmjVihAjezA+PHj8eaNWtw6tQplJaWIhAIDLdZhLuEpjBAluWEiANnzZqFP/3pTzhy5AjOnTs33OYQ7hKa+1nr6uriac9dQa/X4/7770dmZiZKS0vR29tL4tdRgKbBbFVVVQnRQ6rT6WA0GrFq1SpcunQJx44dQzgcToi7AmFwNBUFFixYMKIqWJ8HwzCYP38+vvKVr2Dz5s24fv06EWuCE3M2QJZlhEIh9SyrRKGtrQ3bt28HwzB47rnnMHHixOE2iTBENHlWvV4/4sqtt8PpdGL79u3w+Xz44IMPwHEc2buVoGiqYJWXl9/RCYPDgU6ng8vlwpIlS/Dee+/B5/ORMfAJiubm60TrG6UoCgzDYMmSJZgxYwa2bt2K9vZ24l0TEE15Vr1eHzUmKFHQ6XTIzMzEypUrUVtbi3feeQe9vb3DbRZBI5oWWDdu3IDT6UzYSdQcx6GmpgZbtmxBYWEhvv71rw+3SQQNaFpgpaamJqxQgZt3hqlTp2L27NkoLy9HR0cHiV8TCE1FAZ/Pl9Cd+Er8umzZMrS1teHIkSOkWJBAaCq3/uxnP8PFixfjaU/coWkaM2bMwDe/+U3s2rULn3zyCVlsJQiaFlg+ny/hD1OjKAoGgwGLFi3CypUr8frrrydEvwNBY8z6ta99DcnJyfG0557hcrmwfft28DyPo0ePIhwOEw87wtHUz7phw4YRtRX7TlCmd69evRofffQRrly5MmJ3QRBuosmz3jqOPdGhaRoLFizAgw8+iJ///OekWDDC0ZQN+Pe//51w5dbPg6IopKSkYNmyZbhx4wYOHToEv98/3GYRBkFTNuB3v/sdrly5Ek97hoX77rsPe/bsQUlJCY4fP05SWSMUTWGAcuT6aMNgMGDKlClYvnw5ysrK0NTUROLXEYimBdbLL7+MnJyceNozbNA0jcWLF8NgMOCtt95CKBQiHnaEocmzpqenj9qhvRRFYdKkSVi5ciX27duHiooKUoodYcSsPEmS0NraCqvVOmpP+TMYDJg9ezZWr16NvXv3IisrC1OnTu03d0CW5ZhnEUiShGAwiM7OTgD/f7S9sk/MarWOqgxLPNF0HObGjRvxgx/8ANOnT4+3XcOGLMsQRRHf+973kJKSgl/84hdRcbogCJBlGQzDgKIo9RoMnudx7tw5HDx4EIFAALm5udDpdOju7kZSUhLy8/ORmZk5au9YdxNNv6GrV6+qx7aPVpRml8ceewx79uxBVVUVpk2bhmAwiO7ubkiSpMayFosFycnJsFqtg55NyzAMJkyYgEmTJqG4uBhbt24FRVHw+Xz429/+hitXrqCwsBCZmZn3+qMmHDGLVZnUN378+HjaM2J44IEHsGTJEhQXF8NqtcJkMsFoNKqeVxAE9PT0wO/3IykpSW2fvPUERoqiYLFYkJaWBpZlkZqaCuBmQ/j06dNRXFwMnueH4yMmHDGLVafT4dvf/nY8bRlR2O125OXlYfbs2UhOTobZbAZwM9/M8zwikQjC4TCCwSBaWloQCoXg8XhgNpsHDQuUU74BoK6uDidOnEBubm5C7RYeTjSFAcpUk7GwIOju7gbP85gwYQIMBgMoilKPptfpdFExK03T6O3tRWNjI7xe76A7gDmOQ2VlJQDg/fffR3V1NfLz84flPNxERFM24OjRo3jooYeQlpYWT5uGFVmWIQgC2tvb4Xa7ozzlrYspvV6vClgQBPj9fnR3d8Plcg34H1rZuAgAX/rSl7B//37s3LkTubm5anhAGBxN5dbXX38dn376aTztGXZEUURzczNMJhNsNluUOPt6UpqmwTAMWJYFy7JqvNrY2Niv51cZaGcymeB2u+F2u+H1erFixQoIgoBTp07d64+ZkGgqCmRlZcHpdMbTnmEnEomgra0NRqMRFEWpK/++Gb6+KSuapqHT6dQrFApFNcMoC7JgMIhAIIBAIIBQKITOzk5cuHABHMeNmUXrnRJzGEDTNF599dVRnw9UvOJAQlU85K1thEqSX4k9/X4/0tPT1Tj36tWrOH78OCiKwuHDh2G321FXV4fy8nKsX78eM2bMuIefMHHRJFaHwxFPW0YEPM9Dp9NBkiT1UkKBvvNp+37dN1SgaToqFSXLMmw2G5588smo8u2cOXPwyCOPwOPxJNxIpuEiZrHKsozPPvtMTYKPVhSvqSyalFt938eVS/GyytdKaKDc+hmGgU6ng8fjQXp6er9QQskqEGJD0/igzZs3J9z4IK1QFKUKled5CIIAURT7XX1FO5BwFYErFTGj0QiTyaReRqMRLMuS8w40oCl11dnZOerH7jAMA0EQwHGcKqZbQwElXTWQaCVJgl6vJyKMA5oqWM8999yo7WdVMBqNoGlarVABiCoA9BWrJEmq51X+lWUZVquViDUOxNx1BUD1MKP5D8HzPK5evYpAIKDespXYU/GyimB5nocoiohEIohEIurCKjc3d1TuqBhuNIl1rCAIAmpqaiCKIkwmE1iWVVNTShZACQOUuDYSiUCWZWRnZyMpKWlMlKTvNZorWNevX4+nPSMChmGQmpoKSZIQCoUQDofBcRzC4bDqRW+9RFGExWKBw+Egtf44oWkrtjI5eizgdDrhdrvB8zxCoZAqWuXiOE699YuiCKPRiIyMDLK4iiOaknz33XffmInFDAYDMjMzQVEUOjo61MM/FJS4laZp2Gw2jB8/flTnn0cCmoYJX7t2DcnJybBYLPG2a0SgxKaBQEBttFZO26YoCna7HTabDRaLBQaDgdz+44ymBZYoiv0qOmMFZTHVty+AZVk1rUWIP5o8a319PdLS0tSu+bHGrb8qItJ7i6ZswM6dO1FfXx9Pe0Y0fVsDiVDvPZru5w0NDQiFQvGyhUD4XDSFAefOncOkSZPGzAKLMLLQvMACxsaGQcLIQ1NRQGnWIBCGA039rH/84x/R0NAQT3sIhEHR5FnLy8vR1dUVT3sIhEHRtLt13rx5cLlc8bSHQBgUTdkAJV4l+4YIwwHpZyUkDGOvyE9IWIhYCQkDESshYfg/TiglfZ6/AU4AAAAASUVORK5CYII=)
A simple pendulum is released from
as shown. If
and
represent the mass of the bob and length of the pendulum, the gain in kinetic energy at
is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKsAAACKCAYAAADVGLqKAAAYKUlEQVR4nO2de3BUZ/nHv+fsOXu/5042hKVEbqkFBrACpUiiDKLcUqzOQGlrpVVj6WBVCoLTUnUQm6pltEWHGRipFBR6IUGbhkwZhZQhjUJowqUhhdw25LrJXs6e2+8P5pxfliRlT2BJNnk/M2fIZLO7zyZfnvO8z/O8z0vJsiyDQEgA6OE2gECIFSJWQsJAxEpIGIhYCQkDESshYSBiJSQMzHAbQBi5yLKMSCSC9vZ2+Hw+0DQNnU4HABAEAZFIBDqdDqmpqUhNTYVerwdFUXGzhyJ5VsJAyLKMUCiE1tZWAIDRaIROp4MsyxAEATzPIxwOg+M4iKIIu92O9PR0mM3muAmWeFZCP2RZhiiKaGlpgcFgQFJSkipUURTB87zqVRmGQSgUQkdHBwRBgNfrBcuynytYWZaHJGgiVkI/JEnCjRs3wDAMUlNTodPpQFFUlMhkWYZyU5YkCZIkobe3Fz6fDxkZGWCYgaUliiIikQgMBgNoWtuSiSywCFEot/+Ojg44nU5VqAoURYGmaTAMo14sy4JlWdA0jc7OTkQiEQwUXfI8j5qaGrzxxhtqeKEFIlZCFKIoorOzEzabDSzLRj1GUVTUpSy4FNHqdDqEw2F0dXVBkqSo58qyDI7jcPToUfzmN7/BpUuX+v3M7SBiJUTB8zw4joPBYOj32K3eciDh0jStxq+3PrehoQH19fVYvnw5Lly4gJ6eHk22xRyzSpKE7u7uQV08YXQgCAI4joPVaoUsy5AkKSoMUGLVvjErEC3cUCgEURSjniOKIo4fP441a9agtbUV//znP5GXlweHwxGzbTGLVRRFFBUVoa6uDjRNaw6OCYmB1+tFfn4+HA4HBEFQ/9aKYJXFlCRJ/QTb9+u+nlUURfh8PvT29iI7Oxvjxo3Dvn37cObMGeTk5MScGdAk1oMHD8LpdGLx4sWw2WyDrvgIiYvL5QJN02ouVbm9980CiKIYJdq+4h2IcDiMs2fPwmg04vz582BZFqFQCG+++SbWrFmjLs5uR8xqo2kaHo8HOp0O48aNw+rVq2Gz2WJ9OiFB4DgOra2taoWKpul+KStJkiCKonrd6mkpilIXZ7Iso7e3F5cvX4bVaoUgCBAEAQsXLsTJkydRWVmJmTNnwmQy3da2mMXKMAyKiopQUVGBAwcOYMWKFbDZbGr5jTA6CIfD8Pv9iEQiYBgGNE1DkqQoz6eIUxHercK1Wq3qz4uiiMbGRvA8j0cffRRutxuSJOGhhx5CS0sL3n77beTk5MSUd4058KQoCrm5uVi+fDlmzJiBl19+GT6fb4i/EsJIhWVZmEwmhMNh9YpEIohEIuB5HjzPqyGCIta+XwNAUlISGIaBKIr4+OOPUVRUhObmZoTDYfV9WltbIUkSSktLceTIEfj9/tvapmmV1NPTA7PZjKeffhqNjY0oLi5GMBiMWvkREhuaplWxRSIRtf6vXJFIBBzHRQlXuSRJgtlshsPhiPKs+fn5+OIXv6iGEhRFQZIkLFq0CE888QSsVmtMd+iYG1lEUcS2bdvwxBNPwOv14tChQzh48CC2bduG+++/H0aj8Q5+RYSRhCRJ6OzsxLVr10BRFAwGgxoSKELr2yegiJWmaWRmZiIlJSUu4WHMnlWWZZw/fx5+vx80TWPJkiWYP38+3njjDfT09JDc6yiCoig4nU4kJSVBkiSEQiGEQqGosKCvp+V5HpIkwel0Ijk5OW5pTU0x64oVK5CWlgaapuF0OpGfn4+mpiaUlpZqrkYQRi4URal9qikpKaAoCpFIJEqwilBFUQTLskhLS4PH4wHDMHFrEbyjftaenh6UlpbiD3/4A7Zu3Yr8/Py4Nt8S7j2CIKCnpwc+nw9dXV39Hnc6nUhNTYXD4Yh7ZkiTWJUfVQQpCALC4TC2bNkCjuOwY8cOuFyufg0QhMRFyatKkqT2DSi5VJPJpPYD9K1yxYuYwwBJklBWVob29nb1ewzDwGw249lnn0U4HMbhw4cRCARI/DqKUEIClmVhNpvhdDrVy2g0gmXZfm2E8SJmsYqiiFdeeQWXL1+OfgGaxoQJE1BQUID9+/ejoaFBc+sXIXFQOqyGI9yLWaw0TcPhcMBisfR7TKfTYf78+Vi4cCG2bduGlpaWu2okgQBozAa89NJL8Hq9Az5mtVrx/e9/H5Ik4cCBA+jt7SXFAsJdRZNn/cIXvjBo84rBYMCECRPw+OOP4/3330dlZSUikchdM5RA0LTA8vv9CAQCAz4uiiI4jkN7ezuSk5Px2muvob29ncSvhLuGpgXW5s2b8emnn0IQBLUdTBRF9PT0oLGxER9++CEkScLGjRvB8zyKi4tjalAgEGIhphZBZZvt6dOn4fV61coGAHR1daG4uBiXL1/G1KlTsWbNGhgMBmzcuBE7duyA2+3GI488QooFhDsmpqKAMoVj7969EEURtbW16OjoAADY7XYsWLAACxcuhN1uVydycByHoqIi1NTU4Fe/+hUyMjKg1+vj/oEIo5eYK1jK3KO+jQuyLIOmaZjNZuj1+n7lts8++ww7duxATk4OnnrqKbjdbuJhCUNGU+pKr9fDarXC5XLB7XYjKSkJLpdLnYN0K5mZmVi3bh3ee+89VFdXk1QW4Y7QtMA6dOgQmpqa1CrG7WrCOp0ODzzwAJYuXYrf/va3uHbtGskOEIaMpn7Wffv2oampKeYXpygKFosFTz/9NGw2G/bs2YOenh7iYQlDQlOX7Lhx4wac1PF5sCyLpKQkfPe738WFCxdw6tQpcByn6TUIBEDDAkuZLGc2m4e0BbuzsxMlJSV46623UFRUBK/XS3bGEjShqdyampoKq9U6pDdyOp2YP38+rFYrjh49iu7ubtJKSNCEpjCgt7d3yAKjKAoZGRn40Y9+hNLSUrz99tskdiVoQlM24Pnnn+/Xz6oFlmUxc+ZMFBQU4J133sGlS5dI/EqIGU3ZgKampjvaGEjTNIxGI5YtWwaPx4PDhw+ju7ubpLMIMaEpZn3qqaeQnZ19x2+alpaGJ598EidPnkRFRYXaGEMgfB6aKlhLly6Fy+W64zdlWRY5OTlYtWoV/vKXv+DSpUskfiXcFk0LrDv1gEpDDMdxYFkWjz/+OFJSUvDKK6/A7/cTwRI+F03N13v37sX169eH/GY8z6Ourg7FxcXqnM4NGzagq6sLH3zwAYLB4JBfmzD60bTAKikpQVtbm/o9ZS+5MurwVvpOlpMkCe3t7aioqIDRaERJSQmqqqqQnZ2N9evXY//+/aivrwfP8yR+JQyIpjDA4/GoQ19FUYTf70dNTQ1Onz4Nn88HURTVW31rayv++9//4pNPPkFbWxsikQjq6upgNBoxZ84c5OXl4aOPPoJer8eDDz6IrKwsvPnmmyQ7QBiUmMWq0+mwc+dOTJ48GbIsw+/34+zZs2htbUVJSQl27dqFjo4OSJKEhoYG7N69GzU1Nfj444/x2muvoaWlBX6/H7IsQ6/XIyMjA2azGbIsw+1245lnnsH58+dx4MCBfid9EAiAxmyAy+VSu/17e3sxZcoUzJs3DytWrAAABINBhEIhVFVVgWVZfPWrX0VeXh5aWlpw7tw5MAyDiooK1NfXo7GxEW63GyaTCSzLYtq0aVi3bh2Ki4tRXV0dNXiWQAA0xqwtLS3gOA4URcHj8SAtLQ3BYBAXL14ETdNITk5GMBhEVVUVvF4vLBYLrFYrJk6ciJqaGng8HnAch9///vcoKSnBokWLYDAY1Bn0Dz/8MObMmYO///3vqpcmEBQ0lVt//OMfo7a2FsBNT9vc3Izdu3fjhRdeULescByHYDCI9PR0dWiX1WpFV1cXkpOT8ctf/hIvvvgitm7dqp4MouB2u7F27VpUV1ejrKyMnLlFiELT2UC3Nk7b7Xa1UHDs2DE8/PDDSE9PBwB1B4FyATcHuTmdzkELC3q9HllZWSgoKMA//vEPTJ8+Hbm5uWSjIQGAxnJrYWEhPB4PgJthgcPhwNy5c/Gd73wHixYtQn19PWRZhtFoRG9vrzoqUSkCxLJZ0GKxYO3atcjKysLWrVvh9/tJOEAAoHGBtXjxYrjdbgA3j6BRkvjKlGSHwwGXy4WcnBycP38e4XAYgUAAlZWVmDt3rrpN+3bvo9Pp8Mwzz8Bms6m9rwSCpjxr3wLAyZMnsWvXLnz44YeoqKgARVGYNWsWrFYrvvzlL6O5uRn/+9//UFZWhoyMDMycOTPmEwkpikJWVhY2bNiAd999F5cvXybFAoK2cuuePXvQ2toKWZYxbtw48DyPd999FzzPo6CgQN2jlZ2djR/+8Ic4ffo0/H4/nn/+efUsglix2+2YNWsWJk+ejL179w54LDhhbBHzHixBEPCNb3wDL774IubOnQuO49TT5QwGgzoBGYB6XKIyRdBoNA5pAK3SS7B9+3ZMnz4dmzZtGvK2GkLioylmnTVrFpKSkkBRFIxGI6xWKxwOR78hFzRNg2VZWCwWWCyWIY/xVloJ169fj3/96184c+YMQqGQ5tchjA40HYCh3Ibv9fHt7e3t2LdvH+rq6rBp0yZ4vV4yhmgMokl1yiSWe43dbkdBQQFaW1tx/PhxhEIhEr+OQTQtsM6ePTvgWUjxhmVZpKSk4NFHH8WJEydw9uxZMlV7DKKp3LplyxbU1NTE055BMZvNWLVqFaZMmYJNmzaR7MAYRNM9XTlwdrhQNi1OnjwZf/3rX6MawQmjH03l1p/85CdquXW4SE1NRWFhIf7zn/+gurqaFAvGEHd0dutw4ff78eqrr+LixYvYvXs37Hb7sHp8wr1Bc7l1JGjbbDZj3bp1MBqN+PWvf31HY40IiYOmbMDu3bvR3NwcT3tigmEYTJw4EWvXrsWJEydw8uRJUiwYA2jKBhw7dgxXr16Npz2amDNnDl544QUcOXJkRNlFiA+aNgzm5eUhKysrnvZowmQyYeHChQCAY8eOIRgMkkEZoxhNvQGFhYXIyMiIpz2aYBgGdrsd3/rWt1BZWYmysjIylXAUo0msdrsdLMvG0x7NGI1GLF26FLNnz8azzz6LGzdukMXWKEVTzFpeXj4ij2enKAqPPfYYFi9ejD//+c9obGwcbpMIcUBTNqCoqAgNDQ3xtGfIuFwu/PSnP0VtbS3OnDkzYtJshLuHpjxrKBQasQ0kBoMBWVlZmDdvHvbv349AIEAWW6MMTae11NbWIisra0intdwLBEFAU1MTioqKwHEcXnrpJSQnJ5Pe11GCpt6AadOmjVihAjezA+PHj8eaNWtw6tQplJaWIhAIDLdZhLuEpjBAluWEiANnzZqFP/3pTzhy5AjOnTs33OYQ7hKa+1nr6uriac9dQa/X4/7770dmZiZKS0vR29tL4tdRgKbBbFVVVQnRQ6rT6WA0GrFq1SpcunQJx44dQzgcToi7AmFwNBUFFixYMKIqWJ8HwzCYP38+vvKVr2Dz5s24fv06EWuCE3M2QJZlhEIh9SyrRKGtrQ3bt28HwzB47rnnMHHixOE2iTBENHlWvV4/4sqtt8PpdGL79u3w+Xz44IMPwHEc2buVoGiqYJWXl9/RCYPDgU6ng8vlwpIlS/Dee+/B5/ORMfAJiubm60TrG6UoCgzDYMmSJZgxYwa2bt2K9vZ24l0TEE15Vr1eHzUmKFHQ6XTIzMzEypUrUVtbi3feeQe9vb3DbRZBI5oWWDdu3IDT6UzYSdQcx6GmpgZbtmxBYWEhvv71rw+3SQQNaFpgpaamJqxQgZt3hqlTp2L27NkoLy9HR0cHiV8TCE1FAZ/Pl9Cd+Er8umzZMrS1teHIkSOkWJBAaCq3/uxnP8PFixfjaU/coWkaM2bMwDe/+U3s2rULn3zyCVlsJQiaFlg+ny/hD1OjKAoGgwGLFi3CypUr8frrrydEvwNBY8z6ta99DcnJyfG0557hcrmwfft28DyPo0ePIhwOEw87wtHUz7phw4YRtRX7TlCmd69evRofffQRrly5MmJ3QRBuosmz3jqOPdGhaRoLFizAgw8+iJ///OekWDDC0ZQN+Pe//51w5dbPg6IopKSkYNmyZbhx4wYOHToEv98/3GYRBkFTNuB3v/sdrly5Ek97hoX77rsPe/bsQUlJCY4fP05SWSMUTWGAcuT6aMNgMGDKlClYvnw5ysrK0NTUROLXEYimBdbLL7+MnJyceNozbNA0jcWLF8NgMOCtt95CKBQiHnaEocmzpqenj9qhvRRFYdKkSVi5ciX27duHiooKUoodYcSsPEmS0NraCqvVOmpP+TMYDJg9ezZWr16NvXv3IisrC1OnTu03d0CW5ZhnEUiShGAwiM7OTgD/f7S9sk/MarWOqgxLPNF0HObGjRvxgx/8ANOnT4+3XcOGLMsQRRHf+973kJKSgl/84hdRcbogCJBlGQzDgKIo9RoMnudx7tw5HDx4EIFAALm5udDpdOju7kZSUhLy8/ORmZk5au9YdxNNv6GrV6+qx7aPVpRml8ceewx79uxBVVUVpk2bhmAwiO7ubkiSpMayFosFycnJsFqtg55NyzAMJkyYgEmTJqG4uBhbt24FRVHw+Xz429/+hitXrqCwsBCZmZn3+qMmHDGLVZnUN378+HjaM2J44IEHsGTJEhQXF8NqtcJkMsFoNKqeVxAE9PT0wO/3IykpSW2fvPUERoqiYLFYkJaWBpZlkZqaCuBmQ/j06dNRXFwMnueH4yMmHDGLVafT4dvf/nY8bRlR2O125OXlYfbs2UhOTobZbAZwM9/M8zwikQjC4TCCwSBaWloQCoXg8XhgNpsHDQuUU74BoK6uDidOnEBubm5C7RYeTjSFAcpUk7GwIOju7gbP85gwYQIMBgMoilKPptfpdFExK03T6O3tRWNjI7xe76A7gDmOQ2VlJQDg/fffR3V1NfLz84flPNxERFM24OjRo3jooYeQlpYWT5uGFVmWIQgC2tvb4Xa7ozzlrYspvV6vClgQBPj9fnR3d8Plcg34H1rZuAgAX/rSl7B//37s3LkTubm5anhAGBxN5dbXX38dn376aTztGXZEUURzczNMJhNsNluUOPt6UpqmwTAMWJYFy7JqvNrY2Niv51cZaGcymeB2u+F2u+H1erFixQoIgoBTp07d64+ZkGgqCmRlZcHpdMbTnmEnEomgra0NRqMRFEWpK/++Gb6+KSuapqHT6dQrFApFNcMoC7JgMIhAIIBAIIBQKITOzk5cuHABHMeNmUXrnRJzGEDTNF599dVRnw9UvOJAQlU85K1thEqSX4k9/X4/0tPT1Tj36tWrOH78OCiKwuHDh2G321FXV4fy8nKsX78eM2bMuIefMHHRJFaHwxFPW0YEPM9Dp9NBkiT1UkKBvvNp+37dN1SgaToqFSXLMmw2G5588smo8u2cOXPwyCOPwOPxJNxIpuEiZrHKsozPPvtMTYKPVhSvqSyalFt938eVS/GyytdKaKDc+hmGgU6ng8fjQXp6er9QQskqEGJD0/igzZs3J9z4IK1QFKUKled5CIIAURT7XX1FO5BwFYErFTGj0QiTyaReRqMRLMuS8w40oCl11dnZOerH7jAMA0EQwHGcKqZbQwElXTWQaCVJgl6vJyKMA5oqWM8999yo7WdVMBqNoGlarVABiCoA9BWrJEmq51X+lWUZVquViDUOxNx1BUD1MKP5D8HzPK5evYpAIKDespXYU/GyimB5nocoiohEIohEIurCKjc3d1TuqBhuNIl1rCAIAmpqaiCKIkwmE1iWVVNTShZACQOUuDYSiUCWZWRnZyMpKWlMlKTvNZorWNevX4+nPSMChmGQmpoKSZIQCoUQDofBcRzC4bDqRW+9RFGExWKBw+Egtf44oWkrtjI5eizgdDrhdrvB8zxCoZAqWuXiOE699YuiCKPRiIyMDLK4iiOaknz33XffmInFDAYDMjMzQVEUOjo61MM/FJS4laZp2Gw2jB8/flTnn0cCmoYJX7t2DcnJybBYLPG2a0SgxKaBQEBttFZO26YoCna7HTabDRaLBQaDgdz+44ymBZYoiv0qOmMFZTHVty+AZVk1rUWIP5o8a319PdLS0tSu+bHGrb8qItJ7i6ZswM6dO1FfXx9Pe0Y0fVsDiVDvPZru5w0NDQiFQvGyhUD4XDSFAefOncOkSZPGzAKLMLLQvMACxsaGQcLIQ1NRQGnWIBCGA039rH/84x/R0NAQT3sIhEHR5FnLy8vR1dUVT3sIhEHRtLt13rx5cLlc8bSHQBgUTdkAJV4l+4YIwwHpZyUkDGOvyE9IWIhYCQkDESshYfg/TiglfZ6/AU4AAAAASUVORK5CYII=)
physics-General
Maths-
P(θ) and
are the pts. on the ellipse
then ![C P to the power of 2 end exponent plus C D to the power of 2 end exponent equals](data:image/png;base64,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)
P(θ) and
are the pts. on the ellipse
then ![C P to the power of 2 end exponent plus C D to the power of 2 end exponent equals](data:image/png;base64,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)
Maths-General