Specific Weight Volume Gravity MCQ Quiz in தமிழ் - Objective Question with Answer for Specific Weight Volume Gravity - இலவச PDF ஐப் பதிவிறக்கவும்

Explanation:

The pressure at any point in a static fluid is obtained by Hydro-static law which is given by:

∴ P = ρgh

Rearranging the above equation:

\(h=\frac{P}{\rho{g}}=\frac{P}{γ}\)

where P = pressure above atmospheric pressure h = height of the point from the free surface, and γ = specific weight of the fluid.

Explanation:

• Specific gravity: It is also known as relative density, it is the ratio between the density of an object and a reference substance.
  • The specific gravity can tell us, based on its value, if the object will sink or float in our reference substance.
  • Mathematically it is Specific gravity = Density of substance/density of water.
  • It has no dimension.
  • Usually, our reference substance is water which always has a density of 1 gram per milliliter or 1 gram per cubic centimeter or 1000 kg /m3.
• From the above, it is clear that specific gravity has no dimension. Therefore the dimensional formula of specific gravity is M0L0T0.

Additional Information

• Density: It is defined as the mass of a body per unit volume. We can also say how much mass it can contain in a specific volume.
  • As of dense material like Iron takes more mass in a given volume than of wood.
  • Mathematically it gives a formula Density (ρ) = mass (m) / Volume (V)
  • SI Unit is kg/m3.
  • 1m3 = 1000 liters of water.

Concept:

Mass can be calculated using the characteristic gas equation.

PV = mRT

Calculation:

Given v = 3 m³/s, P = 1.5 bar, T = 300 K,

R (molar based) = characteristic gas constant = 8314 J/kmol-K

M = 28.97,

⇒ R (mass based) = 286.98 J/Kg K

\(m = \frac{{PV}}{{RT}} = \frac{{1.5 \times 100 \times 1000 \times 3}}{{286.98 \times 300}} = 5.2268\;kg/s\)

Density = mass/volume

\(\Rightarrow \rho = \frac{m}{v} = \frac{{5.2268}}{3} = 1.74\;kg/{m^3}\)

W (specific weight) = ρg = 17.09 N/m³

Concept:

Relation between the velocity of sound in fluid (C), Bulk modulus of elasticity (K) and density of fluid (ρ) is:

\(C = \sqrt {\frac{K}{ρ }}\)

Bulk Modulus of Elasticity in terms of pressure changes:

\(K=-\frac{\Delta P}{\frac{\Delta V}{V}}\)

Calculation:

Given:

Density of fluid ρ = 1200 kg/m³, Reduction in volume \(= \frac{{{\rm{\Delta }}V}}{V} \times 100 = 2\%\)

Velocity of sound in fluid C = 1600 m/sec

\(\begin{array}{l} V = \sqrt {\frac{K}{ρ }} \\ 1600 = \sqrt {\frac{K}{{1200}}} \end{array}\)

K = 30.72 × 10⁸ N/m²

We know that bulk modulus of elasticity of a liquid is

\(\begin{array}{l} K = \frac{{ - {\rm{\Delta }}P}}{{\left( {\frac{{{\rm{\Delta }}V}}{V}} \right)}}\\ \Rightarrow {\rm{\Delta }}P = K\left( {\frac{{{-\rm{\Delta }}V}}{V}} \right) = \frac{{30.72 \times {{10}^8} \times 2}}{{100}} \end{array}\)

⇒ 61.44 × 10⁶ N/m²

The weight of the fluid (W) is equal to the mass (m) multiplied by the gravitational acceleration (g). From this formula, we can derive mass as follows:

m = W/g

Here, W is given as 9.81 N and g as 9.81 m/sec², so m = 9.81 N / 9.81 m/sec² = 1 kg.

As we know,

Density (ρ) = mass/volume

Here, the volume of the fluid (V) is 1 litre, which is equal to 0.001 cubic meters (m³), so the density becomes,

ρ = 1 kg / 0.001 m³ = 1000 kg/m³.

So, the answer is (4) 1000 kg/m³.

Specific gravity (S):

Specific gravity is defined as the ratio of the density of the fluid to the density of the standard fluid

\(Specific\, gravity\, (S)={Density\, of\, fluid\over Density\, of\, standard\, fluid}={Specific\, weight\, of\, fluid\over Specific\, weight\, of\, standard\, fluid}\)

Therefore, the dimensional formula of specific gravity is M0L0T0.
We know that:

The density of water (ρ) = 997 kg/m3 or 0.997 kg/lit

\(Specific\, gravity\, of\, water (S_W)={Density\, of\, water\over Density\, of\, water}={0.997\, Kg/lit\over 0.997\, Kg/lit}\)

The specific gravity of water (SW) = 1

Also, we know that the density of mercury is 13600 kg/m3 or 13.6 kg/lit

The specific gravity of mercury (SM) =13.6

Concept:

Weight:

• The weight is the mass of a body multiplied by the acceleration due to gravity.
• The SI unit of weight is Newton (N).
• Formula, Weight, W = mg, where m = mass, g = acceleration due to gravity
• In space, if there is no gravity acting on a body, then the weight of that body becomes zero.
• To define weight, direction, and magnitude are needed. So weight is a vector quantity.
• Weight can vary according to location.
• By using spring balance, weight can be measured.

Explanation:

Weight, W = mg

Simply we can say that the weight is equal to the product of mass and acceleration due to gravity.

Additional Information
Mass:

• It is the measure of the amount of matter in a body. 
• The SI unit of mass is the kilogram (kg)
• A body’s mass does not change at any time.
• The mass has magnitude, so it is a scalar quantity.
• Mass can never be zero.
• By using ordinary balance, mass can be measured.

The correct answer is g/cm3.

Key Points

• The SI unit of mass density is kg/m3.
• The CGS unit of mass density is g/cm3. 
• The density of the material is its mass per unit of volume.

Additional Information 

• The most widely used symbol for density is the ρ (rho), while the Latin letter D can also be used.
• The density is defined mathematically as the mass divided by volume.
• ρ = m/V
• ​The reciprocal density of a material is often referred to as its specific volume, a concept often used in thermodynamics.
• Density is an inefficient commodity in that the volume of a material does not increase its density, instead, it increases its mass.

Explanation:

• 1 litre is equal to 1 cubic decimetre.
• That is the volume of a cube 10 centimetres × 10 centimetres × 10 centimetres.
• 1 L ≡ 1 dm3 ≡ 1000 cm3
• 1 L ≡ 0.001 m3 ≡ 1000 cm3

Concept:

Buoyancy, or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. 

The upthrust exerted by water is exactly equal to the weight of the block.

But when it is exactly pressed down, then more water is displaced.

Hence, the upthrust exerted by water increases.

Solution:

Given:

Mass = 160 g

Specific Gravity of wood = 0.8

Specific Gravity of metal = 10

Density of water = 1gm/cc

The volume of the block of wood = Mass/Density

V = 160 / 0.8 × 1 = 200 cm³

Let the mass of the metal piece is x gm.

The volume of the metal piece

V_metal = x/10 cm³

The total volume of fluid displaced 

V_Total= (200 + x/10) 10^-6 m³

Weight of fluid displaced = V_Total × ρ_f × g

= (200 + x/10) 10^-6 × 1000 × 10

= (200 + x/10) 10-2

If the block floats in water, then

weight $=$ upthrust

(160+x)10 × 10^-3 = (200 + x/10) 10^-2

160 + x = 200 + x/10

x - x/10 = 40

9x/10 = 40

9x = 400

x = 400/9

∴ x = 44.4 gm

The correct answer is option (2).