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JEE Main & Advanced Sample Paper JEE Main Sample Paper-18

  • question_answer
    A homogenous rod of length \[2l\] floating partly immersed in water is supported by a string at one of its ends. If the specific gravity of rod is 3/4, what is the fraction of the length of the rod that extends out of water?

    A)  2/3                       

    B)  3/4

    C)  1/2                       

    D)  4/5

    Correct Answer: C

    Solution :

     Let\[x\]units long portion be inside water. \[\therefore \] \[{{r}_{rod}}gA(2l)\,l\cos \theta ={{\rho }_{water}}gA\,x\left( 2l-\frac{x}{2} \right)\cos \theta \] \[\Rightarrow \] \[\frac{3}{4}2{{l}^{2}}=x\frac{(4l-x)}{2}\] \[\Rightarrow \] \[3{{l}^{2}}=4xl-{{x}^{2}}\] \[\Rightarrow \] \[{{x}^{2}}-4lx+3{{l}^{2}}=0\] \[\Rightarrow \] \[x=l\]


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