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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 in the figure. The specific gravity of the rod is 0.36. The length of the rod that extends out of the water is K L 10 . Find the value of K.

Correct answer

16

Step-by-step solution

Balancing torque about end A M g L c o s θ = B l + 2 L - l 2 c o s θ M g L = ρ . ( 2 L - l ) A g 2 L + l 2 0.36 × 2 L 2 = 4 L 2 - l 2 2 1.44 L 2 = 4 L 2 - l 2 l 2 = 4 L 2 - 1.44 L 2 l 2 = 2.56 L 2 l = 16 10 L ∴ K = 16

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