Mechanical Properties Of Fluids

Question

A hollow sphere of volume V is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water

$\frac{V}{2}$

$\frac{V}{3}$

$\frac{V}{4}$

V

Solution

$\frac{V}{2}$

This difference in pressure between the top and the bottom of the object produces an upward force on it. This is called upthrust.

According to Archimedes Principle, the upthrust on an object in a fluid is equal to the weight of the fluid displaced, so the volume of the object multiplied by the density of the fluid.

When a body (sphere) is half immersed, then

Upthrust = weight of sphere

$\frac{V}{2} \times ρ_{liq} \times g = v \times ρ \times g$

∴ $ρ = \frac{ρ_{liq}}{2}$

When body (sphere) is fully immersed then,

Upthrust = weight of sphere + weight of water pourd in sphere

$V \times ρ_{liq} \times g = V \times ρ \times g + V' \times ρ_{liq} \times g$

V' = $\frac{V}{2}$

Some More Questions From Mechanical Properties of Fluids Chapter

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Mechanical Properties Of Fluids

A hollow sphere of volume V is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water

$\frac{V}{2}$

$\frac{V}{3}$

$\frac{V}{4}$

V

Some More Questions From Mechanical Properties of Fluids Chapter

A jar filled with two non-mixing liquids 1 and 2 having densities ρ₁ and ρ₂ respectively. A solid ball, made of a material of density ρ₃, is dropped in the jar. It comes to equilibrium in the position shown in the figure.
Which of the following is true for ρ₁, ρ₂ and ρ₃?

A capillary tube (A) is dropped in water. Another identical tube (B) is dipped in a soap water solution.Which of the following shows the relative nature of the liquid columns in the two tubes?

A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be

Spherical balls of radius R are falling in a viscous fluid of viscosity η with a velocity v. The retarding viscous force acting on the spherical ball is

If two soap bubbles of different radii are connected by a tube,

A steam of a liquid of density ρ flowing horizontally with speed v rushes out of a tube of radius r and hits a vertical wall nearly normally. Assuming that the liquid does not rebound from the wall, the force exerted on the wall by the impact of the liquid is given by

A wide hose pipe is held horizontally by a fireman. It delivers water through a nozzle at one litre per second. On increasing the pressure. this increases to two litres per second. The firman has now to

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Mechanical Properties Of Fluids

A hollow sphere of volume V is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water V2 V3 V4 V

Some More Questions From Mechanical Properties of Fluids Chapter

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A capillary tube (A) is dropped in water. Another identical tube (B) is dipped in a soap water solution.Which of the following shows the relative nature of the liquid columns in the two tubes?

A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be

Spherical balls of radius R are falling in a viscous fluid of viscosity η with a velocity v. The retarding viscous force acting on the spherical ball is

If two soap bubbles of different radii are connected by a tube,

A steam of a liquid of density ρ flowing horizontally with speed v rushes out of a tube of radius r and hits a vertical wall nearly normally. Assuming that the liquid does not rebound from the wall, the force exerted on the wall by the impact of the liquid is given by

A wide hose pipe is held horizontally by a fireman. It delivers water through a nozzle at one litre per second. On increasing the pressure. this increases to two litres per second. The firman has now to

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A hollow sphere of volume V is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water

$\frac{V}{2}$

$\frac{V}{3}$

$\frac{V}{4}$

V

A jar filled with two non-mixing liquids 1 and 2 having densities ρ₁ and ρ₂ respectively. A solid ball, made of a material of density ρ₃, is dropped in the jar. It comes to equilibrium in the position shown in the figure.
Which of the following is true for ρ₁, ρ₂ and ρ₃?