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Buoyant Force

A body of mas...

Question

A body of mass $10 k g$ and volume $0.5 m^{3}$ is placed in a liquid. What is the density of the liquid when buoyant force is equal to weight of the body? (Take acceleration due to gravity = $10 m / s^{2}$ )

Gravitational force

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Buoyant force

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Both A and B

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Frictional force

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Solution

The correct option is C
Both A and B

Given,

Mass of the body $m$ = $10 k g$

Volume of the body $v_{b}$ = $0.5 m^{3}$

Acceleration due to gravity $g$ = $10 m / s^{2}$

Density of liquid = $ρ$

Weight of the body = $m g$ acting downwards

Buoyant force = $v_{b} ρ g$ acting upwards

$v_{b} ρ g$ = $m g$

Density of liquid $ρ$ = $\frac{m}{v_{b}}$ = $\frac{10 k g}{0.5 m^{3}}$ = $25 k g / m^{3}$

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Write true or false for each statement:

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(e) Relative density of a substance is expressed in g $c m^{-} 3$ .

(f) When a body is immersed in a liquid, the buoyant force experienced by the body is equal to the volume of the displaced by it.

(g) A body experiences the same buoyant force while floating in water or alcohol.

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(i) A body floats in a liquid when its weight becomes equal to the weight of the liquid displaced by its submerged part.

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Q. The weight of a body in air is W g and weight in water is X g.find the buoyant force.also find the volume of the object and the buoyant force when dipped in a liquid of 2g/cc.

Select the correct alternative:

(a) The correct relation is

(i) Density = Mass $\times$ Volume

(ii) Mass = Density $\times$ Volume

(iii) Volume =Denstity $\times$ Mass

(iv) Density = Mass + Volume

(b) The relative density of alcohol is 0.8. Its density is

(i) 0.8 (ii) 800 kg $m^{-} 3$

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(d) The density of aluminium is 2.7 g $c m^{-} 3$ and that of brass 8.4 g $c m^{-} 3$ . The correct statement is :

(i) Equal masses of aluminium and brass have equal volumes

(ii) The mass of a certain volume of brass is more than the mass of equal volume of aluminium

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(iv) Equal volumes of aluminium and brass have equal masses.

(e) A density bottle has a marking 25 mL on it. It means that :

(i) the mass of density bottle is 25g

(ii) the density bottle will store 25 mL of any liquid it

(iii) the density bottle store 25 mL.of water, but more volume of liquid denser than water.

(iv) the density bottle will store 25 mL of water but more volume of liquid lighter than water.

(f) The correct statement is :

(i) The buoyant force on a body is equal to the volume of the liquid displaced by it.

(ii) The buoyant force on a body is equal to the volume of the body

(iii) The buoyant force on a body is equal to the weight of the liquid displaced by it.

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(g) A piece of wood floats on water. The buoyant force on wood will be :

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(h) The weight of a body is more than the buoyant force experienced by it, due to a liquid. The body will :

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A body of mass 10 kg and volume 0.5 m3 is placed in a liquid. What is the density of the liquid when buoyant force is equal to weight of the body? (Take acceleration due to gravity = 10 m/s2)

A body of mass $10 k g$ and volume $0.5 m^{3}$ is placed in a liquid. What is the density of the liquid when buoyant force is equal to weight of the body? (Take acceleration due to gravity = $10 m / s^{2}$ )