NEET Sample Paper NEET Sample Test Paper-15

  • question_answer A frictionless track ABCDE ends in a circular loop of radius R. A body slides down the track from point A, which is at a height \[h=5\,cm.\]Maximum value of R for the body to successfully complete the loop is

    A)  5 cm              

    B) \[\frac{15}{4}\,cm\]

    C)  \[\frac{10}{3}\,cm\]              

    D) \[2\,cm\]

    Correct Answer: D

    Solution :

    For successful completion of the loop the speed of the body at the lowest point must be at least\[\sqrt{5gR}.\]Conserving Mechanical energy between the position A and B, we get \[mgh=\frac{1}{2}m{{(\sqrt{5gR})}^{2}}\] \[\therefore \]    \[h=\frac{5}{2}R\] So, for successful completion of the loop, the value of h must be atleast equal to \[\frac{5}{2}\]R. Or, \[h\ge \frac{5}{2}R\Rightarrow \frac{5R}{2}\le h\] \[\therefore \]\[R\le \frac{2h}{5}=\frac{2\times 5}{5}=2\,cm\] So, the maximum value of R must be equal to 2 cm Hence, the correction option is [d].

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