(b) Given:

$$L\:=\:90m$$

$$\Delta\:=\:5200\:tonnes$$

$$d_{f}=\:4.95m$$

$$d_{a}=\:5.35m$$

$$\rho_{sw}=\:1023kg/m^3$$

$$A_{w}=1100m^2$$

$$G_{ML}=\:95cm$$

$$LCB=\:0.6m\:fwd\:of\:midship\:$$

$$LCF=\:2.2m\:aft\:of\:midship$$

$$when\:vessel\:moves\:into\:fresh\:water\:of\:density\:1002kg/m^3$$

$$new\:drafts\:=\:?$$

$$Change\:in\:mean\:draft\:due\:to\:change\:in\:density\:$$

$$=\:\frac{100\times\Delta}{A_{w}}\left\lbrack\frac{\rho_{s}\:-\:\rho_{r}}{\rho_{s}\times\rho_{r}}\right\rbrack$$

$$=\:\frac{100\:\times5200}{1100}\left\lbrack\frac{1.023\:-\:1.002}{1.023\:\times1.002}\right\rbrack=\:9.68\times10^{-3}m$$

$$Change\:in\:mean\:draft=\:9.7cm$$

$$MCT_{1cm}=\frac{\Delta\:\times GM_{}_{L}}{100\:\times L}$$

$$=\:\frac{5200\:\times95}{100\:\times90}$$

$$MCT_{1cm}=\:54.88\:ton.\:m$$

$$Change\:in\:trim\:when\:vessel\:moves\:from\:SW\:to\:FW$$

$$=\:\frac{\Delta\times FB}{MCT_{1cm}}\left\lbrack\frac{\rho_{s}-\rho_{r}}{\rho_{s}}\right\rbrack$$

$$FB\:=\:LCF\:+\:LCB$$

$$FB\:=\:2.2\:+\:0.6\:=\:2.8m$$

$$=\:\frac{5200\:\times2.8}{54.88}\left\lbrack\frac{1.023\:-\:1.002}{1.023}\right\rbrack\:=\:5.44\:\times10^{-3}$$

$$Change\:in\:trim\:=\:5.45cm\:by\:head$$

$$When\:trim\:by\:head,\:change\:in\:fwd\:draft$$

$$d_{f}=\frac{+t}{L}\left\lbrack\frac{L}{2}+LCF\right\rbrack$$

$$=\:\frac{5.45}{90}\left\lbrack\frac{90}{2}+2.2\right\rbrack$$

$$d_{f}=\:2.858cm$$

$$When\:trim\:by\:head,\:change\:in\:aft\:draft$$

$$d_{a}=\:\frac{-t}{L}\left\lbrack\frac{L}{2}-LCF\right\rbrack$$

$$=\:\frac{-5.45}{90}\left\lbrack\frac{90}{2}-2.2\right\rbrack$$

$$d_{a}=\:-2.59cm$$

New draught fwd = draft fwd + change in mean trim + change in fwd draft

$$=\:4.95\:+\:0.097+0.02858\:$$

$$D_{f}=\:5.076m$$

$$New\:aft\:draft\:=\:5.35+0.097-0.0259\:$$

$$D_{a}=5.421m$$

$$New\:fwd\:draft\:D_{f}=5.076m$$

$$New\:aft\:draft\:D_{a}=\:5.421m$$