A slender homogeneous rod of length $2L$ 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 :
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For rotational equilibrium $B\left(2 L-\frac{x}{2}\right) \cos \theta=m g . L \cos \theta$
$\rho . A . x\left(2 L-\frac{x}{2}\right)=0.75 \rho A .2 L . L$
$2 L x=\frac{x^{2}}{2}=\frac{3}{2} L^{2}$
$-3 L^{2}+4 L x-x^{2}=0$
$x^{2}-4 L x+3 L^{2}=0$
$x=L$
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