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JEE Main & Advanced Sample Paper JEE Main Sample Paper-44

  • question_answer
    A wooden ball of density D is immersed in water of density d to a depth h below the uppermost surface of water and then released. Up to what height will the ball jump out of water?

    A)  \[\frac{d}{D}h\]                                

    B)  \[\left( \frac{d}{D}-1 \right)h\]

    C)  \[h\]                            

    D)  Zero

    Correct Answer: B

    Solution :

     Let the volume of the ball be V. Force on the ball due to up thrust = Vdg Net upward force \[=Vdg-VDg\] Consider the force of bouyancy \[\therefore \]    Upward acceleration is given by \[VDa=Vdg-VDg\] \[\therefore \]    \[a=\left( \frac{d-D}{D} \right)g\] Velocity on reaching the surface, \[v=\sqrt{2ah}\] Further,   \[v=\sqrt{2gH}\] \[\therefore \]    \[2ah=2gH\] or         \[H=\frac{ah}{g}=\,\left( \frac{d-D}{D} \right)h=\left( \frac{d}{D}-1 \right)h\]


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