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 cut and 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. $0.50s$
• D. $0.98s$

Answer 1

The correct option is B $0.63s$

Since two-thirds of the wooden block is immersed in water, its density $=2\rho /3,$ where $\rho$ is the density of water.

Let the volume of the chip be $V$. Then its weight is $\left(2/3\right)V\rho g.$

The upthrust acting on it inside the water is $V\rho g.$ Hence, the unbalanced upward force is $V\rho g(1-2/3)=V\rho g/3$.

Hence, its acceleration $a$ in the upward direction is
$a=\frac{V\rho g/3}{\left(2/3\right)V\rho }=\frac{g}{2}$

If $t$ is the required time, then

$1=0+\frac{1}{2}a{t}^2=\frac{1}{2}\frac{g}{2}{t}^2$

Hence, $t^2=\frac{4}{g}=\frac{4}{10}=0.4$
$t=0.63s$