Home
Class 11
PHYSICS
A uniform vertical cylinder is released ...


A uniform vertical cylinder is released from rest with its lower end just touching the liquid surface of a deep lake. Calculate the maximum displacement of the cylinder in meters. Take `l=4mand (sigma)/(rho)=(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
4

`Al sigmag-Axrhog=Alsigmaa`
`a=g-(rho gx)/(sigmal) , int_(0)^(v)v.dv=int_(0)^(x)(g-(rhogx)/(sigmal))dx`
`implies(v^(2))/(2)=dx-(rhog)/(sigmal)(x^(2))/(2)` at maximum displacement,
`impliesx=(2sigmal)/(rho)=2xx(1)/(2)xx4=4m`
Promotional Banner

Similar Questions

Explore conceptually related problems

A very flexible uniform chain of mass M and length l is suspended vertically in a lift so that its lower end is just touching the surface of the floor. When the upper end of the chain is released, it falls with each link coming to rest the instant it strikes the floor of the lift.Find the force exerted by the floor of the lift on the chain at the moment, when one fourth of the chain has already rested on the floor. Assume that lift is moving up with an acceleration g/2.

A very flexible cahin of length L and mass M is vertically suspended with its lower end just touching the table. If it is released so that each link strickes the table and comes to rest. What force the chain will exert on the table at the moment y part of lenght falls on the table ? .

A uniform slender rod of mass m and length L is released from rest, with its lower end touching a frictionaless horizontal floor. At the initial moment, the rod is inclined at an angle theta=30^(@) with the vertical. Thent he value of normal reaction from the from the floor just after release will be

A uniform rod smoothly pivoted at one of its ends is released from rest. If it swings in vertical plane, the maximum speed of the end P of the rod is. .

A very flexible uniform chain of mass M and length L is suspended vertically so that its lower and just touches the surface of a table. When the upper end of the chain is released it falls with each link coming to rest the instant it strikes the table. Find the force exerted by the chain on the table at the moment when y part of the chain has already rested on the table.

A uniform solid cylinder of density 0.8g//cm^3 floats in equilibrium in a combination of two non-mixing liquids A and B with its axis vertical. The densities of the liquids A and B are 0.7g//cm^3 and 1.2g//cm^3 , respectively. The height of liquid A is h_A=1.2cm. The length of the part of the cylinder immersed in liquid B is h_B=0.8cm . (a) Find the total force exerted by liquid A on the cylinder. (b) Find h, the length of the part of the cylinder in air. (c) The cylinder is depressed in such a way that its top surface is just below the upper surface of liquid A and is then released. Find the acceleration of the cylinder immediately after it is released.