A ring, a disc and a sphere all of the same radius andmass roll down an inclined plane from the same height h. Which of the three reaches bottom (i) earliest (ii) latest ?

A ring, a disc and a sphere all of the same radius andmass roll down a

1.	A ring, a disc and a sphere all of the same radius andmass roll down an inclined plane from the same height h. Which of the three reaches bottom (i) earliest (ii) latest ?
Answer» <html><body><p></p>Solution :The <a href="https://interviewquestions.tuteehub.com/tag/acceleration-13745" style="font-weight:bold;" target="_blank" title="Click to know more about ACCELERATION">ACCELERATION</a> attained by the centre of mass of a rolling body down an inclined plane is <br/> `a =(g sin <a href="https://interviewquestions.tuteehub.com/tag/theta-1412757" style="font-weight:bold;" target="_blank" title="Click to know more about THETA">THETA</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a> + I/(<a href="https://interviewquestions.tuteehub.com/tag/mr-549185" style="font-weight:bold;" target="_blank" title="Click to know more about MR">MR</a>^(2))` <br/> For a ring, `I = MR^(2), a_(r) (g sin theta)/2` <br/> For a disc `I = 1/2 MR^(2), a_(d) = (g sin theta)/(1+1/2) = (2g sin theta)/3` <br/> For sphere, `I = 2/5 MR^(2), a_(s) = (g sin theta)/(1 +2/5) = (5g)/7 sin theta` <br/> Thus, `a_(r) lt a_(d) lt a_(s)`.They all start from rest. So the sphere will reach bottom <a href="https://interviewquestions.tuteehub.com/tag/first-461760" style="font-weight:bold;" target="_blank" title="Click to know more about FIRST">FIRST</a> and the ring last.</body></html>