Step 1: Calculate the buoyancy factor for the drillstring.
The buoyancy factor for steel immersed in drilling fluid is given by:
\[ BF = 1 - \frac{\rho_m}{\rho_s} \]
where $\rho_m$ is the mud density and $\rho_s$ is the density of steel, both expressed in ppg.
For static conditions, the mud density is $10$ ppg:
\[ BF_{\text{static}} = 1 - \frac{10}{65.5} = 0.84733 \]
During circulation, the effective mud density increases to an ECD of $10.75$ ppg:
\[ BF_{\text{circ}} = 1 - \frac{10.75}{65.5} = 0.83588 \]
Step 2: Convert applied WOB to air-equivalent weight.
The applied weight on bit represents the submerged (buoyed) weight of the drillstring under static conditions.
To find the corresponding weight in air:
\[ W_{\text{air}} = \frac{WOB}{BF_{\text{static}}} = \frac{50000}{0.84733} = 59009.01 \text{ lbf} \]
Step 3: Determine the buoyed weight during circulation.
When circulation starts, the increased mud density reduces the buoyancy factor, which changes the submerged weight:
\[ W_{\text{circ}} = W_{\text{air}} \times BF_{\text{circ}} = 59009.01 \times 0.83588 = 49324.32 \text{ lbf} \]
Step 4: Evaluate the change in hook load.
The additional buoyancy caused by circulation results in a reduction in hook load.
This reduction is calculated as:
\[ \Delta H = WOB - W_{\text{circ}} = 50000 - 49324.32 = 675.68 \text{ lbf} \]
Rounding to one decimal place:
\[ \boxed{675.7 \text{ lbf}} \]