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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 16

  • question_answer
    A cone of height h and base of radius r is submerged in a fluid as shown in the figure such that half of its height is outside the fluid. The angle of contact between the fluid and cone is 6 and surface tension for the fluid is T. The net force experienced by cone due to surface tension is

    A) \[\pi rT\cos \theta \]                    

    B) \[\pi rT\sin \theta \]

    C) \[\pi rT\cos \left[ \theta -{{\tan }^{-1}}\left( \frac{r}{h} \right) \right]\]

    D) \[\pi rT\cos \left[ \theta -{{\tan }^{-1}}\left( \frac{h}{r} \right) \right]\]

    Correct Answer: C

    Solution :

    [c] \[dF=Tdl\] Horizontal components will cancel out. \[F=\int{dF\,\cos \,\,\left( \theta -\alpha  \right)}=\int{Td\ell \,\cos \,\left( \theta -\alpha  \right)}\] \[=T\cos \,\,\left( \theta -\alpha  \right)\int{d\ell }=T\cos \left( \theta -\alpha  \right)2\pi r'\] Since only \[\frac{h}{2}\] portion is inside the fluid, \[\therefore \,\,\,r'=\frac{r}{2}\] or         \[F=\pi rT\cos \left[ \theta -{{\tan }^{-1}}\left( \frac{r}{h} \right) \right]\]


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