Question

A uniform rod $AB,12m$ long weighing $24kg,$ is supported at end $B$ by a flexible light string and a lead weight (of very small size) of $12kg$ attached at end $A.$ The rod floats in water with one-half of its length submerged. For this situation, mark out the correct statement.
[Take $g=10m/s^2,$ density of water $=1000kg/m^3]$

• A. The tension in the string is $36g$
• B. The tension in the string is $12g$
• C. The volume of the rod is $6.4\times {10}^{-2}{m}^3$
• D. The point of application of the buoyancy force is passing through C (centre of mass of rod)

Answer 1

The correct option is C The volume of the rod is $6.4\times {10}^{-2}{m}^3$

$T+U=W_1+W_2=360$ N (i)
$U=\frac{V}{2}{\rho }_{w}g=\left(V/2\right)\left({10}^3\right)\left(10\right)$
or $U=0.5\times {10}^4$ V (ii)
($\sum$ Moments) about M=0
$\therefore$ $120\left(\frac{l}{4}\right)+T\left(\frac{3l}{4}\right)=240\left(\frac{l}{4}\right)$
or $T=\frac{240-120}{3}=40$ N$=4$ g
Now from Eqs. (i) and (ii)
$V=6.4\times {10}^{-2}$ m${}^3$