JEE Main & Advanced AIEEE Solved Paper-2013

  • question_answer
    A uniform cylinder of length L and mass M having cross - sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged n a liquid  of density \[\sigma \] at equilibrium position. The extension\[{{x}_{0}}\]of the spring when it is in equilibrium is: (Here, k is spring constant)   AIEEE Solevd Paper-2013    

    A) \[\frac{Mg}{k}\]                              

    B) \[\frac{Mg}{k}\left( 1-\frac{LA\sigma }{M} \right)\]

    C) \[\frac{Mg}{k}\left( 1-\frac{LA\sigma }{2M} \right)\]      

    D) \[\frac{Mg}{k}\left( 1+\frac{LA\sigma }{M} \right)\]

    Correct Answer: C

    Solution :

    \[\left( K{{x}_{0}}+\frac{LA}{2}\sigma g \right)=mg\] \[\therefore \] \[{{x}_{0}}=\frac{Mg}{k}\left( 1-\frac{LA\alpha }{2M} \right)\]


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