NEET Sample Paper NEET Sample Test Paper-16

  • question_answer A body of radius R and mass m is rolling horizontally without slipping with speed u. It then rolls up a hill to a maximum height \[h=\frac{3{{u}^{2}}}{4g}.\]The body might be

    A) solid sphere                 

    B) hollow sphere

    C)      disc                

    D)      ring

    Correct Answer: C

    Solution :

    Total \[K.E=\frac{1}{2}m{{u}^{2}}+\frac{1}{2}I{{\omega }^{2}}=\frac{1}{2}m{{u}^{2}}+\frac{1}{2}I..\frac{{{u}^{2}}}{{{R}^{2}}}\] \[\left[ \because \,\omega =\frac{u}{r} \right]\] According to the law of conservation of energy loss in \[K.E.=\]gain in P.E. or \[\frac{1}{2}\left( m+\frac{1}{{{R}^{2}}} \right){{u}^{2}}=mgh=mg\left( \frac{3{{u}^{2}}}{4g} \right)\] Solving this we get\[I=\frac{1}{2}M{{R}^{2}}\] the solid body is a disc. Hence, the correction option is (c).

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