Home
Class 11
PHYSICS
Consider a solid cylinder of the density...

Consider a solid cylinder of the density `rho_(s)` cross section area A and h ploating in a liquid of density `rho_(l)` as shown in figure `(rho_(l) gt rho_(s))` . It is depressed sligtly and allowed to oscillation.

Text Solution

Verified by Experts

At equilibrium the net force on the cylinder is zero in the vertical direction.
`F_("net") = B - W = 0, B = ` the buoyancy and W = the weight of the cylinder direction.
When the cylinder is depresed slightly by x, the buoyancy increases from `B to B + sigma B`, where `sigma B = |x| rho_(l) Ag`
The equation of motion is, therefore.
`rho, Ah (d^(2)x)/(dt^(2) = - (rho_(l) g)/(rho_(s) h)`
and the angular frequency, `omega`, is
`omega = sqrt((g rho_(l))/(h rho_(s)))`
Promotional Banner

Topper's Solved these Questions

  • LINEAR AND ANGULAR SIMPLE HARMONIC MOTION

    CENGAGE PHYSICS ENGLISH|Exercise Solved Example|15 Videos

  • LINEAR AND ANGULAR SIMPLE HARMONIC MOTION

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 4.1|23 Videos

  • KINETIC THEORY OF GASES AND FIRST LAW OF THERMODYNAMICS

    CENGAGE PHYSICS ENGLISH|Exercise Interger|11 Videos

  • MISCELLANEOUS KINEMATICS

    CENGAGE PHYSICS ENGLISH|Exercise Interger type|3 Videos

Similar Questions

Explore conceptually related problems

A solid cylinder of denisty rho_(0) , cross-section area A and length l floats in a liquid rho(gtrho_(0) with its axis vertical, . If it is slightly displaced downward and released, the time period will be :

The pressure inside a liquid of density rho at a depth h is :

A body of density rho sinks in a liquid of density rho_(L) .The densities rho and rho_(L) are related as:

A cylindrical piece of cork of base area A and height h floats in a liquid of density rho_(1) . The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period T=2pisqrt((hrho)/(rho_(1)g))

A cylindrical piece of cork of base area A and height h floats in a liquid of density rho_(1) . The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period T=2pisqrt((hrho)/(rho_(1)g))

A ball of density rho is released from deep inside of a liquid of density 2 rho . It will move up

A body weighs W_(1) in a liquid of density rho_(1) and W_(2) in a liquid of density rho_(2) . What is the weight of body in a liquid of density rho_(3) ?

A body of density rho is immersed in a liquid of density rho_(L) .State condition when the body will (i) float (ii) sink in liquid.

A body of density rho floats with volume V_(1) of its total volume V immersed in a liquid of density rho_(1) and with the remainder of volume V_(2) immersed in another liquid of density rho_(2) where rho_(1)gtrho_(2) . Find the volume immersed in two liquids. ( V_(1) and V_(2) ).

A ball of volume V and density rho_(1) is moved downwards by a distance 'd' in liquid of density rho_(2) . Find total change in potential energy of the system.