A solid cylinder of density ρ0, cross-section area A and length l floats in a liquid of density ρ(ρ0) with its axis vertical, as shown. If it is slightly displaced downward and released, the time period will be

Question

A solid cylinder of density ρ0, cross-section area A and length l floats in a liquid of density ρ(>ρ0) with its axis vertical, as shown. If it is slightly displaced downward and released, the time period will be (A) 2 π √(l/g) (B) 2 π √(ρ0 I/ρ g) (C) 2 π √(ρ l/ρ0 g) (D) 2 π √(l/2 g)

Tardigrade Admin · Accepted Answer

The time period of a floating uniform cylinder is simply given as R = l

Q. A solid cylinder of density $ρ_{0}$ , cross-section area $A$ and length $l$ floats in a liquid of density $ρ (> ρ_{0})$ with its axis vertical, as shown. If it is slightly displaced downward and released, the time period will be

$2 π \frac{l}{g}$

$2 π \frac{ρ _{0} I}{ρ g}$

$2 π \frac{ρl}{ρ _{0} g}$

$2 π \frac{l}{2 g}$

The time period of a floating uniform cylinder is simply given as $R = l$

Q. A solid cylinder of density ρ0​, cross-section area A and length l floats in a liquid of density ρ(>ρ0​) with its axis vertical, as shown. If it is slightly displaced downward and released, the time period will be

2πgl​​

2πρgρ0​I​​

2πρ0​gρl​​

2π2gl​​