Turito Academy

Test Prep

Global form fields

To keep the mass M steady, let T is the tension in the string joining the two. Then for particle <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABUAAAAMCAYAAACNzvbFAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAKlJREFUeNpjYECAeiAuB2JxIJ4ExC+B+DkQe0HlBYG4D4jfAfEnIK5kIAKsghp8BogjgZgFiOWB+D4QSwLxQSAOh4rLAvEPqAPwgltAvBfqImTwFIhn4xCXxGcgExB/A2IuEsXxAnMg3k8FcRQACsP5VBBHAaDYTqOCOApYh5R0yBFfDsT/gTgAWREo7XFg0UysOFZDqQGW4/AV2cAAiK9AMwbVgDRy7gIAWjAoKUeM/uYAAABTdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPm08L21pPjxtbz4sPC9tbz48L21hdGg+yOpfKQAAAABJRU5ErkJggg==" class="Wirisformula" alt="m comma" width="21" height="12" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»m«/mi»«mo»,«/mo»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="T equals fraction numerator m v to the power of 2 end exponent over denominator R end fraction open parentheses i close parentheses" width="84" height="39" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»T«/mi»«mo»=«/mo»«mfrac»«mrow»«msup»«mrow»«mi»m«/mi»«mi»v«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«mi»R«/mi»«/mrow»«/mfrac»«mfenced separators=¨|¨»«mrow»«mi»i«/mi»«/mrow»«/mfenced»«/math»'/> For mass <img src="data:image/png;base64,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" class="Wirisformula" alt="M comma" width="20" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»M«/mi»«mo»,«/mo»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="T equals M g left parenthesis i i right parenthesis" width="74" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»T«/mi»«mo»=«/mo»«mi»M«/mi»«mi»g«/mi»«mo»(«/mo»«mi»i«/mi»«mi»i«/mi»«mo»)«/mo»«/math»'/> From Eqs. (i) and (ii) <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALsAAAAtCAYAAAD2rxo0AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAc1CXO0QAABRlJREFUeNrtnF1IFUEUxwe5DyIiSYWKRBESERKCRYqEQhIREhKECj0ERYT4ECFpRFREFAUVFUVERIgFFQkR9iARERFBWGSE+FD0UCJF31iUZOdwz+K27HpnZ3dndveeHxxczx3v3h3/O3vOmbkjBMPIUQw2nXAzgnXy32CPwKpYS7GnGuwNd4M6BWCdYMPcFbGnFewud0NwfnEXxJ6dYOe5G4LRCPaAuyH2nAHr5m5Qp4Ji9sXcFbHnPtg6H0/q5hxt8PUpCmVVowHM+96BPQEbBJsf185bAnaHBM/EH0xOl0q0qyIRnp2lDVZ23oK9UPwseI7nDt9hsGNxHdHxTixhDSWCQrA/YBnJRBaFOD5LmwvU5lqAZLnf4WsDu6x6gfvBesDKwE6DTdAFrKfXS8FOgH0C+wa2h/wbXT4Ics/2t4OSowQTD+rARnzqZhRslUf4giP6QWpnp4hG5w8UptykJ0SPyzmc+cNBSqKVuE5v+hSsg+7qhfQ4q6Ckso38C+jDlXk8YhoprrKITcGfkaId7IYP3bRSWHHYRcxjYDW2dhYZ0lQPHaPtori+1eUcG2y/l9DNVaZ6gWM0Gpc6/JgQXPTwW/H3pCPxeCyRsDDxpRfsuA/dVNKoPup47bTtBhildhb7XG4O6/0qPHwZSppxnmaT6sUVkGCLfPrt4l5Ox+sElxaTDtbXu3zoxmLcFq42gL0kgTrbWW3nurzfDxfflCMqWB3k4vCuvB/Af8V2p2FIU896STQPwZoUdHOBwhIrfKn1aFdL55DRm9NXH7QK0+GR2cr6O+kDYKw1xFpJPJ/ByhV000y52ilHiOJsh0WNPkm9ufmGKJ9UAmOr7QH8WHW5RY+tGtZKopkD9l1RNxhyYKXulfi/bOlsh8mmWxkSb4CtEhqsp2hCiVtipkyo4i+i6sxt1kriwcFqJIBu+mzhi1c7rKZM2AZG/HmTih6NkhrEYsoylQvE2nlhQP8XkV0WGjd0TGWniS0eIYYf3ci0w9EdZ1Vx2TeWu9eKbL29QPIcOLoP8r9rBh1T2WnjANghA+etFuozrIzQM5WdNvpodI8SLE+eEzP19JUiu0CQZ9kDoGMqW4ZuIbcuSGbpRdTgnElTxOcopsQTa+qTFI5Us1yDfddQx1S2DHspVGqQCLtyLb0Iq2+8+EkVGSZh6JjK9iO8aXrf2RJhk0svynOEfKkeMZP8TXAdU9l+uUTX2p8jjDC19KKOzp8k3aRqcaHqReqYylYRwdEcI7ufpRdhC2CbyC76YxKGjqnssGN2RNfSC7eE8KTg750mEh1T2X6qMcWSbXUsvWimUb/S4R9QTMAZw+iYyo6CqJdeoNA/k9g7Ha89E7y2KZHomMqOiiiXXuAXM1rAXoNdtfkzdBNw2dGDRG1vEDC+TdsM6wCFdBaLBG9350mitjfwQb5MZe8G+2r7vUnMXm3Ka0Lf3iAm5MtU9kJ6KlvJ+g7B2915Evr2Box2cPnDGjrG7e66ItaLylYtsSD07Q0Y7bwX2do6gltntEesF5WtWmJBqNsbMEZ4KGZmi0ciDteCbNVilNC3N2CMcATsIx3LbnenqpcgW7UYJfTtDRgjrKFBa5HIziPo0ouq3wihb2/AGOMvFRWGNOtFxW+E0Lc3YIzxlZLDy5r1ouI3QujbGzDGGKacq9eAXvz6jcDbG6SHKyT2FgN68etnmEC0kdhXcFcwaWceib2Yu4LJBwa4C5h8YTN3AZMvpDKE+QfGjzs4waeqEgAAASZ0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1zdXA+PG1yb3c+PG1pPm08L21pPjxtaT52PC9taT48L21yb3c+PG1uPjI8L21uPjwvbXN1cD48bWk+UjwvbWk+PC9tZnJhYz48bW8+PTwvbW8+PG1pPk08L21pPjxtaT5nPC9taT48bW8+JiN4MjdGOTs8L21vPjxtaT52PC9taT48bW8+PTwvbW8+PG1zcXJ0PjxtZnJhYz48bXJvdz48bWk+TTwvbWk+PG1pPmc8L21pPjxtaT5SPC9taT48L21yb3c+PG1pPm08L21pPjwvbWZyYWM+PC9tc3FydD48L21hdGg+ldrtewAAAABJRU5ErkJggg==" class="Wirisformula" alt="fraction numerator m v to the power of 2 end exponent over denominator R end fraction equals M g ⟹ v equals square root of fraction numerator M g R over denominator m end fraction end root" width="187" height="45" style="vertical-align:-17px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«msup»«mrow»«mi»m«/mi»«mi»v«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«mi»R«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»M«/mi»«mi»g«/mi»«mo»⟹«/mo»«mi»v«/mi»«mo»=«/mo»«msqrt»«mfrac»«mrow»«mi»M«/mi»«mi»g«/mi»«mi»R«/mi»«/mrow»«mrow»«mi»m«/mi»«/mrow»«/mfrac»«/msqrt»«/math»'/> <img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/905499/1/911824/Picture450.png" alt="" width="136" height="136" />

A particle of mass <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAKCAYAAAC9vt6cAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAI5JREFUeNpjYECAeiAuB2JxIJ4ExC+B+DkQe0HlBYG4D4jfAfEnIK5kQAOroIacAeJIIGYBYnkgvg/EkkB8EIjDoeKyQPwDahkc3ALivVCbkMFTIJ6NQ1wSxmEC4m9AzIWmiJA4HJgD8X4GTEC0OMjP87EoJFocFOppWBQSLb4OKbrIEgfFLQcWhaSKkw4A8RgiEla1vLMAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPm08L21pPjwvbWF0aD5oJvHsAAAAAElFTkSuQmCC" class="Wirisformula" alt="m" width="16" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»m«/mi»«/math»'/> is rotating in a horizontal circle of radius <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJ5JREFUeNpjYMAEP4D4PxA/BeKTQLwNiEWxqGNQAeILaGKtQNyFTXEAEC9FEwsH4vnYFNcDcQmaWCMQF2BTvAqI/ZD4fEB8A4jFsSm+BcSSQMwCxB5AfA6IQ7EpZALiP9CQgGFbBhzAHIj3I/EtcYUCCERi8fVuIJbHpngSEKehiYFMX4hN8Tog9sIivheItdAF3wExBxbFltAoJw0AAKDiG/NA/rdGAAAASXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5SPC9taT48L21hdGg+SC/J9gAAAABJRU5ErkJggg==" class="Wirisformula" alt="R" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»R«/mi»«/math»'/> and is attached to a hanging mass <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAANCAYAAAB2HjRBAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAMNJREFUeNpjYEAFP4DYhQE/AMn/AWImZEEVIP4PxFPwaOQB4odAfAldIgCILwDxczyaZ0LVLEeXqAficiC+AcTmOJwLsrERqg4FrILa3grFyIALiG8BsQGSOhQAkpSG2noDTW4SkoE3oOrgABRy35D4IH9rQNnWQHwFiFmwqAMDkG370QKmHMm5xjjUgUEkEM9HC5yTQDwBzf/o6uB+SkPzxicgvgZ1Li51YLAOiL3QxBYjORefOoZ3QMzBQBgQq44wAAAH+yrmTEDtWAAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+TTwvbWk+PC9tYXRoPttYuhkAAAAASUVORK5CYII=" class="Wirisformula" alt="M" width="15" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»M«/mi»«/math»'/> as shown in the figure. The speed of rotation required by the mass <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAKCAYAAAC9vt6cAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAI5JREFUeNpjYECAeiAuB2JxIJ4ExC+B+DkQe0HlBYG4D4jfAfEnIK5kQAOroIacAeJIIGYBYnkgvg/EkkB8EIjDoeKyQPwDahkc3ALivVCbkMFTIJ6NQ1wSxmEC4m9AzIWmiJA4HJgD8X4GTEC0OMjP87EoJFocFOppWBQSLb4OKbrIEgfFLQcWhaSKkw4A8RgiEla1vLMAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPm08L21pPjwvbWF0aD5oJvHsAAAAAElFTkSuQmCC" class="Wirisformula" alt="m" width="16" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»m«/mi»«/math»'/> keep <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAANCAYAAAB2HjRBAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAMNJREFUeNpjYEAFP4DYhQE/AMn/AWImZEEVIP4PxFPwaOQB4odAfAldIgCILwDxczyaZ0LVLEeXqAficiC+AcTmOJwLsrERqg4FrILa3grFyIALiG8BsQGSOhQAkpSG2noDTW4SkoE3oOrgABRy35D4IH9rQNnWQHwFiFmwqAMDkG370QKmHMm5xjjUgUEkEM9HC5yTQDwBzf/o6uB+SkPzxicgvgZ1Li51YLAOiL3QxBYjORefOoZ3QMzBQBgQq44wAAAH+yrmTEDtWAAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+TTwvbWk+PC9tYXRoPttYuhkAAAAASUVORK5CYII=" class="Wirisformula" alt="M" width="15" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»M«/mi»«/math»'/> steady is <img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905499/1/911824/Picture468.png" alt="" width="142" height="134" />

Solution for the question - a particle of mass 1 is rotating in a horizontal circle of radius r and isattached to a hanging mass m as shown in the figure. the s