Physics-
General
Easy
Question
A particle originally at a rest at the highest point of a smooth circle in a vertical plane, is gently pushed and starts sliding along the circle. It will leave the circle at a vertical distance
below the highest point such that
![](data:image/png;base64,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)
The correct answer is: ![h equals fraction numerator R over denominator 3 end fraction](data:image/png;base64,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)
From law of conservation of energy, potential energy of fall gets converted to kinetic energy.
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/905363/1/914766/Picture269.png)
![therefore blank P E equals K E](data:image/png;base64,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)
![m g h equals fraction numerator 1 over denominator 2 end fraction m v to the power of 2 end exponent](data:image/png;base64,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)
![o r blank v equals square root of 2 g h end root blank open parentheses i close parentheses](data:image/png;base64,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)
Also, the horizontal component of force is equal centrifugal force.
![therefore blank m g cos invisible function application theta equals fraction numerator m v to the power of 2 end exponent over denominator R end fraction open parentheses i i close parentheses](data:image/png;base64,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)
From Eq. (i)
![therefore blank m g cos invisible function application theta equals fraction numerator 2 m g h over denominator R end fraction blank open parentheses i i i close parentheses](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMIAAAAjCAYAAADG+dUWAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAABKdJREFUeNrtm19EXnEYx3+SJIlMXsnEZJIkJkmym8nM5BWTmV0kZmYyM7KLmV1EutjFzG5mZiaRpItkTJIkkUmSGZkukkQXkyTRnkffV2e//X7nnPe87znn7T3Ph0ed53R+531//54/vyelhGKhk2SS5A/JCckayYOYP9MRSYkMjRAlCyT3SSpx3USyBF0cNJCsy7AIhUB9jJMxTTIuQyAUCscG3WuSIZIUyTuSPZJdkju4X03yluQArtZL7fkKklGSfbTPLtl7tKm/4wra2kN7gzIkQtR0wD3SmcBEXYXrVArr8ZukFm5WH/RXMdlTeLYU94fwO8tzklNYAf0diyQ9iBXq0FaFDI0QFeUkKwiidX6RzGHnd7JD8tGir8Xvr0iGLW3WatczjpglwwGshCCEDk/kaZJuwz3emY8Mu7KXPsOuYSLz3xwarvW2SrW2BCE0rmERNFjut5PMB9TfgKvj9Ww7LI7JVZuXIRLCphGujZsPzjHB54D6XpKvPp7N9h2CkDdSCFBLPf6Os0SPAuo56DWlRHlxDGjP9FvaGsjhOz4hGclDX42gLaEImYFF8GJKXaRJs9VXqfM0aCuu+eckgumbObzDDy0ky3nsryW0KYRIJwadJ8gCfOawOXMRJ5y1KTc871fPVmFbnZdxrCIg31f/llJk+w6/E7fVcs9UyuGls8U7Qp5oxyLIdHgNyVYRf99mFf4Jcqsyn4coZS7l8KtbxIIQQoCL3eo03bciMcPsen1QF+cFbZigjSG/l0+xn4bQ7mA2MYfJvOaLKI76M67KAv6GzfpD7f5dkk2Y+02Yfx1OS87DvNr65JYlKzKeg29cSFRinA7RD7OwCGHDG0mXxxwKouN07lwhLIQojvpbsVDScFeuk4xprsyWY0Cbcd2hfdZVywJxwqnLXkuQ2B3Atw+z7y8TvAmWucyhdEBdGdqOnSiO+ieVe6HXJCyCbiGmDYFWtcf32XSZzCmZz4E59ZhDdQF1Cl5ArERx1J/ZTaqy3G1MO0Vaudf3l1h2l5IQd52zIpGgC0GfE9noCmYhRHHUr3x09FkWHVQJS7UJF8tJyuJvtsHq5DKZxTUyu0am8farKxjXKIqjfoX4IB8WwQkH7T8MnT1lCeb6ZS7nxHdlrqI1jbdfnWew7LYLpXEvH3njKI76MwGsV4zQY/ieUx5u3YnBWqxpumosmDKZyzlhS5+aSjb86hTaHI17IURx1M9w2nMbViTzzyGfNNeFs0RNuG7BdafLZx+wmNoNx6Lj3PqyIRAXssd2oGaaK351ShXIgVoUR/3OjlxB0LVmsAA8WX+irQ1Dms25QXAbs1pmSjkW0RraWVfe6VbBP8vq/0NJ01zxqyvaEosojvqTxjEW/w42Et4AamL6LFJ0ZyCuo/4k0WCIeYbdfOoIeKzyU4Y9aolDLx1xHfUnCXYPxzRdn5J/rBESBqd9X2i6NyTPpGuEJDGhBftVSChIqYiQKDI1W1zMeFudn4fck24RkgSnoDlN7Czz6JJuEZKGXpvDpQij0i1C0jDV5nC9T710jZAkTPVebBW+SNcIScJWm8OVmk3SPUJSsNV7sVWYLcYv/BdytqwsIYkeHwAAAXJ0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjIzNDs8L21vPjxtaT4mI3hBMDs8L21pPjxtaT4mI3hBMDs8L21pPjxtaT4mI3hBMDs8L21pPjxtaT5tPC9taT48bWk+ZzwvbWk+PG1pPmNvczwvbWk+PG1vPiYjeDIwNjE7PC9tbz48bWk+JiN4M0I4OzwvbWk+PG1vPj08L21vPjxtZnJhYz48bXJvdz48bW4+MjwvbW4+PG1pPm08L21pPjxtaT5nPC9taT48bWk+aDwvbWk+PC9tcm93PjxtaT5SPC9taT48L21mcmFjPjxtaT4mI3hBMDs8L21pPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93PjxtaT5pPC9taT48bWk+aTwvbWk+PG1pPmk8L21pPjwvbXJvdz48L21mZW5jZWQ+PC9tYXRoPmDZ7oEAAAAASUVORK5CYII=)
From ![increment A O B comma](data:image/png;base64,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)
![cos invisible function application theta equals fraction numerator left parenthesis R minus h over denominator R end fraction](data:image/png;base64,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)
![⟹ m g open parentheses fraction numerator open parentheses R minus h close parentheses over denominator R end fraction close parentheses equals fraction numerator 2 m g h over denominator R end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALwAAAAnCAYAAAC16CIrAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAZpE86XgAABR9JREFUeNrtXVFkHEEYHnGiKkJERFSVijoVFariRFVfKvJQVapO9SFKVFVVhaioqiqRhz6cyEtFVUSIqD5ElIiIiCpV1YeqUtWHigpRFREVrv/Pf6y1szOzdzOzMzcfH8nM3s3MN//O/v/M7BxjzYc7wMmc13GS6hkQIDTm6ZT8M8B3jrRli+rLQyXcFM2N88BPwILAiPo5eQfAKvAX8D1wBdilqa77wBbBNWeBmyn52M7PwAsGNR4ELgH/Av+R3jcs97uMlt7hKPBHijEzytvi5PVS50XxDDiloa69ZKgy2CTD56GP2t1mSOcNYDlS3mnStGyp31W09ApPgTOCa9B473LyrgDnY2nXgS811BXLWpC89p5EvFGh9tvCCYtGp6KlN0C34w/wmOC6t+T2JOExcCyW9gR4X0N9saxxYCfwOfA3cJeMO44ScE3wfT3kYnRZ7IODlHZ2002J7dwGDlN+B7V/l+r/MOGpjYPUDn3/EsVn4xm19AYTwDmJ61DUVk7eIvBy5P924FfqrEZjkTpqk8psoZv1gDo5ilaqtwizwEeW9C9xXMVaOz+Qy1Ogp8EPukk36CmK6cep/d2R+GSDjLlAfAA8pFE9i5be4EvKyB3FYUreN+oEFHYI+BF4TVN9sazlBL97l0aqOP5JBpNfLWh/hAL8QU4712gkjwInBV5w0nvo70cUQ/H6KauWzuMUPfJYHQbfQnnVCEU3UFWCvLL2EkafAs02sIwGz+hxXjSoPRrsG+AlTjv3E9opSq9hO8Fga9rVo6XzGEkINlVdmgHgeuwRPaWpvgMcn7wUq4OqS8NIhxFDup8kY+9Naed6xnTedGz8s6paeoFXwNuS165yHr3lhNmYVfI3G40yZ+aHly4TtNZwi/TQjSK5JEcb2M5o+lVOTBb/rGoZXmA5EvWLwJuWxBmE0QRD02E8Fc4oXCGDjeOuwtMGY48VzXp3U6BYkGjnaMZ0DD6TphrnYhqpaukF0H+XnY7jLTy95tw0OLKebnB9eWXx0kULT1G0KcQz9QwwRQ3tjKa3UzzSH+m3JQpqL9RRhhdQXVbGfTRnEiL6Ixx3otEjJq+spHTR1gImCPx0QDZIV2lnUjqO8j8pYP9AgfFOrK9Vy/ACVcXrfdo8Vs+MjmvoY024otoIg2cU5OZ9e/AUx9fVoUfegC4TbhOpzbefo5u/aKMyY+RjycDE0nI13PPeGXwb2cseuWgrNMJbwQT5VoMS15pYWg4GL2fwWRfKmkY0GT4TBIwmlpaDwfs3wucSsyTuvGDGQOfSskwHVz2kaYP3XjfZL5hMGeFNLC2HES24NLnx4U0sLQeDDy6NkVkamdfJTCwthw4OBp8bmFhaDh0cDD43MLG0HDo4GLy34C0tH+agbiaP9xDBxa0FedLPClSWlm2fSWLyeA8RXHzTJ0/6WYPK0jKOCh0W62ryeA8ROpn+7cE+6+cEcH/2kMXyTR7vIcIw0/8CiM/6OQEcCUYslm/yeA8RRh0cGfOknxO4yeTOpNEFk8d7iLBg+eZ3XT8ngMd0/LZUdpbjPXRih1naM+6Jfs4AzzUsWSjX5PEeIlxkdg5i8kU/p4BBz6yFck0e7yECunUPHeu3POnnFHA6TuYw1UbD5PEeacCXZ/aYe0fL5UU/J4HTW9OGyzR5vEca8GWaJw72WV70cxL4Qsl3pv6Wfz0webwHD7ixzuQPIvimn9PAPfqin7zxCa0UsIeZjSYG+oQzTdJWdOFuhy5Xw39XZyUvcuAXogAAAUR0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjdGOTs8L21vPjxtaT5tPC9taT48bWk+ZzwvbWk+PG1mZW5jZWQgc2VwYXJhdG9ycz0ifCI+PG1mcmFjPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93PjxtaT5SPC9taT48bW8+LTwvbW8+PG1pPmg8L21pPjwvbXJvdz48L21mZW5jZWQ+PG1pPlI8L21pPjwvbWZyYWM+PC9tZmVuY2VkPjxtbz49PC9tbz48bWZyYWM+PG1yb3c+PG1uPjI8L21uPjxtaT5tPC9taT48bWk+ZzwvbWk+PG1pPmg8L21pPjwvbXJvdz48bWk+UjwvbWk+PC9tZnJhYz48L21hdGg+nqhfkAAAAABJRU5ErkJggg==)
![⟹ blank 3 h equals R](data:image/png;base64,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)
![⟹ h equals fraction numerator R over denominator 3 end fraction](data:image/png;base64,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)
Related Questions to study
physics-
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/486109/1/914752/Picture526.png)
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/486109/1/914752/Picture526.png)
physics-General
Physics-
A small mass
is attached to a massless string whose other end is fixed at
as shown in the figure. The mass is undergoing circular motion in the
plane with center at
and constant angular speed
. If the angular momentum of the system, calculated about
and
are denoted by
and
respectively, then
![](data:image/png;base64,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)
A small mass
is attached to a massless string whose other end is fixed at
as shown in the figure. The mass is undergoing circular motion in the
plane with center at
and constant angular speed
. If the angular momentum of the system, calculated about
and
are denoted by
and
respectively, then
![](data:image/png;base64,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)
Physics-General
chemistry-
The monomer used to produce neoprene is
The monomer used to produce neoprene is
chemistry-General
chemistry-
What is ‘A’ in the following reaction?
![](data:image/png;base64,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)
What is ‘A’ in the following reaction?
![](data:image/png;base64,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)
chemistry-General
chemistry-
What is ‘A’ in the following reaction?
![](data:image/png;base64,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)
What is ‘A’ in the following reaction?
![](data:image/png;base64,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)
chemistry-General
Physics-
Three identical particles are joined together by a thread as shown in figure. All the three particles are moving in a horizontal plane. If the velocity of the outermost particle is
, then the ratio of tensions in the three sections of the string is
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905325/1/914718/Picture524.png)
Three identical particles are joined together by a thread as shown in figure. All the three particles are moving in a horizontal plane. If the velocity of the outermost particle is
, then the ratio of tensions in the three sections of the string is
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905325/1/914718/Picture524.png)
Physics-General
physics-
A weightless thread can bear tension up to
wt. A stone of mass
is tied to it and revolved in a circular path of radius
in a vertical plane. If
, then the maximum angular velocity of the stone will be
A weightless thread can bear tension up to
wt. A stone of mass
is tied to it and revolved in a circular path of radius
in a vertical plane. If
, then the maximum angular velocity of the stone will be
physics-General
physics-
A man 80 kg is supported by two cables as shown in the figure. Then the ratio of tensions
and
is
![](data:image/png;base64,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)
A man 80 kg is supported by two cables as shown in the figure. Then the ratio of tensions
and
is
![](data:image/png;base64,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)
physics-General
Maths-
A square matrix
for
and
(constant) for
is called a
A square matrix
for
and
(constant) for
is called a
Maths-General
chemistry-
DS for the reaction: MgCO3(s) → MgO(s) + CO2(g) will be -
DS for the reaction: MgCO3(s) → MgO(s) + CO2(g) will be -
chemistry-General
physics-
A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out length
where
is in metre and t is in second. The radius of the path is 20 m. The acceleration of P when t =2s is nearly
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486112/1/914450/Picture518.png)
A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out length
where
is in metre and t is in second. The radius of the path is 20 m. The acceleration of P when t =2s is nearly
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486112/1/914450/Picture518.png)
physics-General
chemistry-
For the reaction N2(g)+3H2(g)→2NH3(g),DH is-
For the reaction N2(g)+3H2(g)→2NH3(g),DH is-
chemistry-General
physics-
Three identical spheres of mass
each are placed at the corners of an equilateral triangle of side 2
. Taking one of the corner as the origin, the position vector of the centre of mass is
Three identical spheres of mass
each are placed at the corners of an equilateral triangle of side 2
. Taking one of the corner as the origin, the position vector of the centre of mass is
physics-General
physics-
Four bodies of equal mass start moving with same speed are shown in the figure. In which of the following combination the centre of mass will remain at origin?
![](data:image/png;base64,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)
Four bodies of equal mass start moving with same speed are shown in the figure. In which of the following combination the centre of mass will remain at origin?
![](data:image/png;base64,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)
physics-General
chemistry-
From the reactions: C(s)+2H2(g)→CH4(g)DH=–XK cal C(g)+4H(g)→CH4(g),DH=–X1Kcal CH4(g)→CH3(g)+H(g)DH=+Y(Kcal) Bond energy of C–H bond is-
From the reactions: C(s)+2H2(g)→CH4(g)DH=–XK cal C(g)+4H(g)→CH4(g),DH=–X1Kcal CH4(g)→CH3(g)+H(g)DH=+Y(Kcal) Bond energy of C–H bond is-
chemistry-General