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<img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/905475/1/911606/Picture279.png" alt="" width="130" height="106" /><br />To reach the unshaded portion particle <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIVJREFUeNpjYMAEP4D4PxR/AeJVQOyIRR2DChBfQOKzAbELEN8HYi10xQFAvBSLIclAXIIuWI9NEAg6gDgHXRDkPj80MVEgvgXEwuiKQYKSSHxjID6KzYNMQPwHGgrvoIqa0TTDgTkQ72cgEkQC8XxiFU8C4jRiFa8DYi9iFYM8xcFALQAAM/sYFg8AKnAAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPlA8L21pPjwvbWF0aD4oc3y9AAAAAElFTkSuQmCC" class="Wirisformula" alt="P" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»P«/mi»«/math»'/> needs to travel horizontal range greater than <img src="data:image/png;base64,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" class="Wirisformula" alt="R sin invisible function application 45 degree" width="60" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»R«/mi»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mn»45«/mn»«mo»°«/mo»«/mrow»«/mrow»«/math»'/> or <img src="data:image/png;base64,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" class="Wirisformula" alt="left parenthesis 0.7 blank R right parenthesis" width="48" height="16" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»(«/mo»«mn»0.7«/mn»«mi» «/mi»«mi»R«/mi»«mo»)«/mo»«/math»'/> but its range is less than <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAAjCAYAAAB2KjFhAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAQRJREFUeNpjYCAMfgDxfyB+CsQngXgbEIsykAFUgPgCmlgrEHeRY1gAEC9FEwsH4vnkGFYPxCVoYo1AXECOYauA2A+JzwfEN4BYnBzDbgGxJBCzALEHEJ8D4lByDGIC4j/QmIRhWwYygTkQ70fiW5IbiyAQiSXWdgOxPDmGTQLiNDQxkOsWkmPYOiD2wiK+F4i1SDXsHRBzYBG3hGapUTCYwX8K8CgY7MAaiNcA8Scg/gWtpaLJNewgtEzjgfJBJcVRqBhVAKhgvERN7/+glkGWUK9SDDigbQ1rSg0SBOINQOxGqUFKUINUKDVIA4hnAzEXpQaJQ9saLNQI8C1Ql9G8sMQKABIHQKehtwsFAAAAYnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bWk+UjwvbWk+PG1uPjI8L21uPjwvbWZyYWM+PC9tYXRoPn2KCiIAAAAASUVORK5CYII=" class="Wirisformula" alt="fraction numerator R over denominator 2 end fraction" width="19" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»R«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«/math»'/>. So it will fall on shaded portion<br /><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAOCAYAAAD0f5bSAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAALtJREFUeNpjYMAO3IB4BxB/A+IfQHwYiB0Z8IAOIN4AxKZAzATFfkD8EoitsWnIA+KZOAwD2XQcXVAWiK9ATcYFPgAxG7JAKxDnMOAHu4HYAFkAZIs8AU0PgZgLxmGChhQ+wAJ1HorAJwKagoB4IbrgNwKBcBTdPwxQUxJxaKgE4i5sEhpA/BiI46HOBQE9IF4MDVmcwByI90OTDgj/B+IsBhJBOBA/B+IzQJwMxKLEauQB4nIgvgZNyAwAqaghgYyCZAkAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPlE8L21pPjwvbWF0aD715aU4AAAAAElFTkSuQmCC" class="Wirisformula" alt="Q" width="13" height="14" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»Q«/mi»«/math»'/> is near to origin, its velocity will be nearly along <img src="data:image/png;base64,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" class="Wirisformula" alt="Q R" width="23" height="14" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»Q«/mi»«mi»R«/mi»«/math»'/> so its will fall in unshaded portion

Solution for the question - consider a disc rotating in the horizontal plane with a constant angularspeed d theta about its centre o . the disc has a shaded reg