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JEE Main & Advanced JEE Main Paper (Held on 08-4-2019 Afternoon)

  • question_answer
    A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights \[{{h}_{sph}}\]and \[{{h}_{cyl}}\]on the incline. The ratio \[\frac{{{h}_{sph}}}{{{h}_{cyl}}}\]is given by :-   [JEE Main 8-4-2019 Afternoon]

    A) \[\frac{14}{15}\]                    

    B) \[\frac{4}{5}\]

    C) 1                     

    D)   \[\frac{2}{\sqrt{5}}\]

    Correct Answer: A

    Solution :

    for solid sphere \[\frac{1}{2}m{{v}^{2}}+\frac{1}{2}.\frac{2}{5}m{{R}^{2}}.\frac{{{V}^{2}}}{{{R}^{2}}}=mg{{h}_{sph.}}\] for solid cylinder \[\frac{1}{2}m{{v}^{2}}+\frac{1}{2}.\frac{1}{2}m{{R}^{2}}.\frac{{{V}^{2}}}{{{R}^{2}}}=mg{{h}_{cyl.}}\] \[\Rightarrow \]\[\frac{{{h}_{sph.}}}{{{h}_{cyl.}}}=\frac{7/5}{3/2}=\frac{14}{15}\] 


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