Question

A slender homogeneous rod of length $2L$ floats partly immeresed in water, being supported by a string fastened to one od its end, as shown. The length of rod that extends out of water is-

• A. $L$
• B. $L/2$
• C. $L/4$
• D. $3L$

Answer 1

The correct option is B $L/2$

Let $h$ be height of root inside water

$A=$ area of cross section

$d=$ density of root

$d_w=$ density of water

mass of rod $=$ mass of mass displaced

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

$h=2l\times d/d_w=21\times 0.75=3L/2$

Height of rod outside water $=\frac{1}{2}$.