Question

A wooden block with a coin placed on its top, floats in water as shown in figure.
The distance l and h are shown in the figure. After some time the coin falls into the water. Then

• A. $h$ decreases
• B. $l$ decreases
• C. $h$ increases
• D. $l$ increases

Answer 1

Answer: (A), (B)

$l$ decreases

$\left(a\right)$ When coin falls into water, block rises up since total weight i.e. block and coin decreases and upthrust remains almost same as the volume displaced by coin is comparatively small and therefore $l$ decreases
$\left(b\right)$ When the coin falls in water, volume of water displaced by coin is equal to the volume of coin $V_1\left(say\right)$.

When coin is at the top of wooden block, it displaces volume of water $V_2,$
Which is more than $V_1,$ because weight of coin = weight of volume of water displaced by coin
or
${\rho }_c{V}_{1}g={\rho }_1{V}_{2}g$

$\Rightarrow \frac{V_2}{V_1}=\frac{{\rho }_c}{{\rho }_1}$

$\therefore {\rho }_c>{\rho }_1$

$\therefore V_2>V_1$

Hence $h$ decreases.

Final Answer$:\left(A\right),\left(B\right)$