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A tube is fixed in a vertical plane as shown in figure .Form point A a sphere of mass 0.314 kg is released .During its motionin the tubeitfacesa constant resistiveforce R . At B itsvelocitybecomes zero . Calculate(i) theconstant resistiveforce R and (if) work done byresistive force (average radisu of semicircularpath is 1 m ) .

Answer» <html><body><p></p>Solution :Let D be the lowest point on its path . Let us assume that the potential energy at D to zero , so potential energy at A is , <br/> `v_(A) = mgr ""….(1)` <br/> `v_(<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a>) = (mgr)/2 ""……(2)`<br/> ` [ :. "In right <a href="https://interviewquestions.tuteehub.com/tag/triangle-1427233" style="font-weight:bold;" target="_blank" title="Click to know more about TRIANGLE">TRIANGLE</a> " Delta OB. B , angle <a href="https://interviewquestions.tuteehub.com/tag/obb-2881761" style="font-weight:bold;" target="_blank" title="Click to know more about OBB">OBB</a> = 30^(@) and OB = r ."Theoppositeside of " 30^(@) " in right triangle is the half value of diagonal "] ` <br/> Work <a href="https://interviewquestions.tuteehub.com/tag/done-2591742" style="font-weight:bold;" target="_blank" title="Click to know more about DONE">DONE</a> by constant resistive force R , <br/> `W_(R) = " Force " xx " displacement " `<br/> ` = R xx arc AB ` <br/> ` = R xx theta xx r ` <br/> ` = R xx (pi/2 +pi/3) r ` <br/> ` :. W_(R) = R xx (5pi)/6 r "".....(3)` <br/>Now `V_(A)=V_(B) +W_(R)`<br/> ` mgr = (mgr)/2 +R (5pi)/6 r ` <br/> ` [ :. " From equation (1) ,(2) and (3) "] `<br/> ` :. (mgr)/2= R xx (5pi)/5 r ` <br/> ` :.R = (3mg)/(5pi)` <br/> ` = (3xx0.314 xx10)/(5xx3.14)` <br/> ` :. R = 0.6 N ` <br/> Work doneby resistiveforce R,<br/> `W_(R) = R xx` displacement<br/> ` = R xx arcAB ` <br/> ` = R xx(5pir)/6` <br/>` = (0.6 xx 5xx 3.14 xx1)/6` <br/> ` :. W_(R) = 1.57 J`</body></html>


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