Question

A wooden block in the form of a uniform cylinder floats with one-third length above the water surface. A small chip of this block is held at rest at the bottom of a container containing water to a height of $1m$ and is then released. The time in which it will rise to the surface of water is $(g=10m/s^2)$

• A. $0.84s$
• B. $0.63s$
• C. $0.5s$
• D. $1s$

Answer 1

The correct option is B $0.63s$

The wooden block floats with one third length above the water surface. we have

$V{\rho }_{wood}g=\frac{2V}{3}{\rho }_{water}g\Rightarrow {\rho }_{wood}=\frac{2}{3}{\rho }_{water}$

Acceleration of the block in upward direction is given by

$a=g\left(\frac{{\rho }_{water}-{\rho }_{wood}}{{\rho }_{wood}}\right)\Rightarrow a=\frac{g}{2}$

$\Rightarrow 1=\frac{1}{2}\left(\frac{g}{2}\right)t^2\because s=ut+\frac{1}{2}a{t}^2\Rightarrow t^2=0.4\Rightarrow t=0.632s\approx 0.63s$