BITSAT 2017 Slot 2 Solved Paper

Let block is displaced through x m, then weight of displaced water or upthrust (upwards)
=−Axρg
Where, A is area of a cross-section of the block and ρ is density. This must be equal to force (= ma) applied wherem is mass of the block and a is acceleration.
∴ ma=−Axρg
∴ a=−

Aρg

m

x=−ω2x
This is equation of SHM.
The time period of oscillation,
T=

2π

ω

=2π√

m

Aρg

⇒ T∝

1

√A