A block of wood is floating on water with its dimensions 50cm x 50 cm x 50cm inside the water. The buoyant force acting on the block is X N. Find X.  (Consider,  g =9.8 m/s² )

We know that when an object is immersed in liquid, it displaces liquid and the volume of the displaced liquid is equal to the volume of the object.
$\therefore$The volume of water displaced = $50\times 50\times 50\times {10}^{-6}{m}^3=0.125m^3$
The density of water, $\mathrm{\rho }=1000\mathrm{kg}{/\mathrm{m}}^3$

Density =$\frac{\mathrm{Mass}}{\mathrm{Volume}}$; Weight = Mass x acceleration due to gravity (g)

$\therefore$Weight of water displaced  = Volume x Density x Gravity 

$\Rightarrow$Weight of water displaced = $0.125\times 1000\times 9.8=1225N$

According to Archimedes' principle, the buoyant force acting on an object is equal to the weight of the liquid displaced. 

Weight of water displaced = Upthrust
$\Rightarrow$1225 N = X N

Therefore, the value of X will be 1225.