You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Buoyant Force

A large tank ...

Question

A large tank of area A contains liquid of density $ρ$ . A cylinder of density $\frac{ρ}{4}$ and length ℓ, and area a $(a ≪ A)$ is kept in equilibrium by applying an external vertically downward force. The cylinder is just submerged in liquid. At t = 0 the external force disappears instantaneously. Answer the following questions.

The maximum height attained by centre of mass of cylinder from the liquid surface.

3 \frac{l}{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3 \frac{l}{4}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

l

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{l}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $3 \frac{l}{2}$
Velocity of cylinder as it just comes out of water.
$v = \sqrt{2 g l}$ by work energy theorem
Hence height above the surface of liquid = ℓ
Total height $= ℓ = \frac{l}{2} = \frac{3 l}{2}$

Suggest Corrections

Similar questions

Q. A large tank of area A contains liquid of density

ρ

. A cylinder of density

\frac{ρ}{4}

and length ℓ, and area a

(a ≪ A)

is kept in equilibrium by applying an external vertically downward force. The cylinder is just submerged in liquid. At t = 0 the external force disappears instantaneously. Answer the following questions.

The acceleration of cylinder at the instant t = 0 is

Q. A large tank of area A contains liquid of density

ρ

. A cylinder of density

\frac{ρ}{4}

and length ℓ, and area a

(a ≪ A)

The time taken by the cylinder to just come out form the liquid

Q. A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density

ρ

at equilibrium position. When the cylinder is given a small downward push and released, it starts oscillating vertically with a small amplitude. If the force constant of the spring is 'k', the frequency of oscillations of the cylinder is?

Q. Two non-mixing liquids of densities

ρ

and

n ρ (n >

1) are put in a container. The height of each liquids

h

. A solid cylinder of length

L

and density

d

is put in this container. The cylinder floats with its its axis vertical and length

p L (p < 1)

in the denser liquid. The density

d

is equal to

A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half-submerged in a liquid of density $ρ$ at equilibrium position. When the cylinder is given a small downward push and released it starts oscillating vertically with a small amplitude. If the force constant of the spring is k, the frequency of oscillation of the cylinder is :

Join BYJU'S Learning Program

The correct option is A 3l2Velocity of cylinder as it just comes out of water. v=√2gl by work energy theorem Hence height above the surface of liquid = ℓ Total height =ℓ=l2=3l2

The correct option is A $3 \frac{l}{2}$
Velocity of cylinder as it just comes out of water.
$v = \sqrt{2 g l}$ by work energy theorem
Hence height above the surface of liquid = ℓ
Total height $= ℓ = \frac{l}{2} = \frac{3 l}{2}$