A plank of mass 'm' and area of cross - section `A` is floating as shown in figure. When slightly displaced from mean position, plank starts oscillations. Find time period of these oscillations.

Answer

A, B

Explanation

Three force are acting on the plank :
(i) weight
(ii) spring force
(iii) upthrust
Weght is a constant force. So, it will not contribute in the time period. Spring force and upthrust are variable forces. when displaced downwards from the mean position, both forces increase.
So, their force constants are additive
`:. k_(e) = k + rhoAg`
`:. T = 2pi sqrt ((m)/(k_(e))`
`= 2pi sqrt((m)/(k + rho Ag))`.