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A slender homogeneous rod of length 2 \mathrm{~L} floats partly immersed in water, being supported by a string fastened to one of its ends, as shown. The specific gravity of the rod is 0.75 . The length of rod that extends out of water is

Option: 1

\mathrm{\mathrm{L}}


Option: 2

\mathrm{\frac{1}{2} \mathrm{~L}}


Option: 3

\mathrm{\frac{1}{4} \mathrm{~L}}


Option: 4

\mathrm{3L}


Answers (1)

best_answer

\mathrm{\begin{aligned} & \mathrm{mg}=\mathrm{A} .2 \mathrm{~L} \times 0.75 \times \mathrm{g} \\ & \mathrm{T}+\mathrm{A} \times \mathrm{g}=\mathrm{A} .2 \mathrm{~L} \times 0.75 \mathrm{~g} \\ & \mathrm{~T}=\mathrm{Ag}[1.5 \mathrm{~L}-\mathrm{x}] \\ & \mathrm{A} \times \mathrm{g} \cos \theta\left(\ell-\frac{\mathrm{x}}{2}\right)=\mathrm{T} \cos \theta \ell \\ & \mathrm{x}\left(\ell-\frac{\mathrm{x}}{2}\right)=\ell[1.5 \mathrm{~L}-\mathrm{x}] \quad \mathrm{x}=\ell \end{aligned}}

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Ritika Harsh

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