Question

A slender homogenous rod of length $2$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?

• A. L
• B. $\frac{1}{2}$L
• C. $\frac{1}{4}$L
• D. $3$L

Answer 1

The correct option is B $\frac{1}{2}$L

let h be height of rod inside water. A = area of cross section.
d = density of rod, $d_w$ density of water

mass of rod = mass of water displaced

$d\times A\times 2L=d_w\times h\times A$

$h=2L\times \frac{d}{d_w}=2L\times 0.75=\frac{3L}{2}$

Height of rod outside the water $=\frac{L}{2}$