JEE Main & Advanced Sample Paper JEE Main Sample Paper-7

  • question_answer
    A time varying force \[F=2t\] acts on a spool as shown. The angular momentum of the spool at time t about the lower most point in contact with the ground is

    A)  \[\frac{{{r}^{2}}{{t}^{2}}}{R}\]                  

    B)  \[\frac{{{(R+r)}^{2}}{{t}^{2}}}{r}\]

    C)  \[(R+r){{t}^{2}}\]                            

    D)  Depends on mass

    Correct Answer: C

    Solution :

    Torque \[=\vec{r}\times \vec{F}=(R+r)\times 2t\] Since \[L=\int_{{}}^{{}}{\tau dt}\] we get \[L=\int_{{}}^{{}}{2(R+r)tdt=2(R+r)\frac{{{t}^{2}}}{2}=(R+r){{t}^{2}}}\]


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