Answer
9 children
Work Step by Step
We can write,
The float's weight is $W_{f}$ = 20g
The weight of the displaced water is $W_{w}=m_{w}g=\rho_{water}V_{sub}g$
By Archimedes' principle, $W_{w}$ is equal in magnitude to the buoyancy force, which balances gravity when the slab is in equilibrium.
Let's find the minimum weight required to fully merge the float.
$W=\rho_{water}V_{sub}g=1000\space kg/m^{3}\times1.8\times2.4\times0.1\space m^{3}g\space m/s^{2}$
$W=432g\space N$
Total weight of children = (432g - 20g)N = 412g N
Nos. of children required to $=\frac{412g}{50g}=8.24$
fully emerge the boat
So 9 children required to fully emerge the boat
