<P> The period of roll can be estimated from the following equation </P> <Dl> <Dd> T = 2 π k g G M _̄ (\ displaystyle T = (\ frac (2 \ pi \, k) (\ sqrt (g (\ overline (GM))))) \) </Dd> </Dl> <Dd> T = 2 π k g G M _̄ (\ displaystyle T = (\ frac (2 \ pi \, k) (\ sqrt (g (\ overline (GM))))) \) </Dd> <P> where g is the gravitational acceleration, k is the radius of gyration about the longitudinal axis through the centre of gravity and G M _̄ (\ displaystyle (\ overline (GM))) is the stability index . </P>

Discuss the significance of metacentric height in ship design