MECHANICAL PROPERTIES OF FLUIDS MCQs for NEET UG PHYSICS — Medium, Page 8

211 Medium

211 of 218

Remembering +4 | -1

Shear modulus is zero for

View answer and explanation

Correct option: C

Gases

Option C (Gases) is correct because gases do not have a definite shape and cannot resist shear stress, hence their shear modulus is zero.

Solution approach

Correct Answer + Core Reason: Gases. Gases cannot resist shear stress, so their shear modulus is zero.

Step-by-Step Solution:

Step 1: Understand the concept of shear modulus.

Step 2: Shear modulus (G) is a measure of a material's resistance to deformation by shear stress.

Step 3: Solids have a definite shape and can resist shear stress, so they have a non-zero shear modulus.

Step 4: Liquids can resist shear stress to some extent, but gases cannot.

Step 5: Gases do not have a definite shape and cannot resist shear stress, so their shear modulus is zero.

Why other options are wrong:
- Option A: Solids - Solids have a non-zero shear modulus.
- Option B: Liquids - Liquids have a shear modulus, although it's smaller than solids.
- Option D: Liquids and gases - Liquids do have a shear modulus, even though it's small.

Key Concepts:
- Shear Modulus
- Shear Stress
- States of Matter

Memory Aids:
- Gases have no resistance to shear.

Quick Tips:
- Remember that shear modulus measures resistance to shear stress.

212 Medium

212 of 218

Analyzing +4 | -1

If there were a reduction in gravitational effect, which of the following forces do you think would change in some respect?

View answer and explanation

Correct option: D

Archimedes uplift

Option D (Archimedes uplift) is correct because Archimedes' principle depends on the gravitational force acting on the fluid.

Solution approach

Correct Answer + Core Reason: Archimedes uplift. Archimedes' uplift (buoyant force) is directly proportional to the weight of the fluid displaced, which depends on the gravitational effect.

Step-by-Step Solution:

Step 1: Define Archimedes' principle: The buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

Step 2: Express the buoyant force mathematically: $F_B = V \times \rho \times g$ , where $V$ is the volume of the fluid displaced, $\rho$ is the density of the fluid, and $g$ is the acceleration due to gravity.

Step 3: Analyze the effect of reducing the gravitational effect (reducing $g$ ). If $g$ decreases, then the buoyant force $F_B$ also decreases.

Step 4: Consider the other forces:
- Magnetic force: Independent of gravity.
- Electrostatic force: Independent of gravity.
- Viscous force: While viscosity itself is a property of the fluid, the force due to viscosity might indirectly be affected by changes in pressure gradients which could be linked to gravity, but the primary dependence is on gravity for buoyancy.

Step 5: Conclusion: The Archimedes uplift (buoyant force) is the most directly affected by a reduction in the gravitational effect.

Why other options are wrong:
- Option A: Magnetic force is caused by moving charges and is independent of gravity.
- Option B: Electrostatic force is caused by electric charges and is independent of gravity.
- Option C: Viscous force depends on the fluid's viscosity and the velocity gradient, not directly on gravity.

Key Concepts:
- Archimedes' Principle
- Buoyancy
- Gravitational force

Memory Aids:
- Buoyant force = weight of fluid displaced.

Quick Tips:
- Remember that buoyant force is directly proportional to the gravitational acceleration.
- Consider how each force is defined and what factors it depends on.

213 Medium

213 of 218

Application +4 | -1

Two substances of densities

{\rho _1}

and

{\rho _2}

are mixed in equal volume and the relative density of mixture is 4. When they are mixed in equal masses, the relative density of the mixture is 3. The values of

{\rho _1}

and

{\rho _2}

are

View answer and explanation

Correct option: A

{\rho _1} = 6and{\rho _2} = 2

Option A (

{\rho _1} = 6 and {\rho _2} = 2

) is correct because it satisfies both conditions: equal volume and equal mass mixing, leading to the given relative densities of the mixtures.

Solution approach

Correct Answer + Core Reason: ${\rho _1} = 6 and {\rho _2} = 2$ . These densities satisfy the conditions for both equal volume and equal mass mixing.

Step-by-Step Solution:

Step 1: Define relative density.\nRelative density is the ratio of the density of a substance to the density of a reference substance, usually water. Let the density of water be $\rho_w = 1$ .

Step 2: Equal volume mixing.\nWhen mixed in equal volumes, the density of the mixture is given by:
$\rho_{mix} = \frac{V \rho_1 + V \rho_2}{V + V} = \frac{\rho_1 + \rho_2}{2}$ \nThe relative density is 4, so $\frac{\rho_1 + \rho_2}{2} = 4$ , which means $\rho_1 + \rho_2 = 8$ .

Step 3: Equal mass mixing.\nWhen mixed in equal masses, the density of the mixture is given by:
$\rho_{mix} = \frac{m + m}{\frac{m}{\rho_1} + \frac{m}{\rho_2}} = \frac{2}{\frac{1}{\rho_1} + \frac{1}{\rho_2}} = \frac{2 \rho_1 \rho_2}{\rho_1 + \rho_2}$ \nThe relative density is 3, so $\frac{2 \rho_1 \rho_2}{\rho_1 + \rho_2} = 3$ , which means $2 \rho_1 \rho_2 = 3(\rho_1 + \rho_2)$ .

Step 4: Solve the equations.\nWe have two equations:
1. $\rho_1 + \rho_2 = 8$
2. $2 \rho_1 \rho_2 = 3(\rho_1 + \rho_2) = 3(8) = 24$ \nSo, $\rho_1 \rho_2 = 12$ .\nWe need to find two numbers that add up to 8 and multiply to 12. These numbers are 6 and 2.\nSo, $\rho_1 = 6$ and $\rho_2 = 2$ (or vice versa).

Why other options are wrong:
- **Option B ( ${\rho _1} = 3 and {\rho _2} = 5$ ):** 3 + 5 = 8, but 3 * 5 = 15, not 12.
- **Option C ( ${\rho _1} = 12 and {\rho _2} = 4$ ): 12 + 4 = 16, not 8.
- Option D (None of these): The correct answer is one of the options.

Key Concepts:
- Density of mixture (equal volume)
- Density of mixture (equal mass)
- Relative density

Memory Aids:
- Remember the formulas for mixing densities in equal volumes and equal masses.

Quick Tips:**
- When solving mixture problems, set up the equations carefully and solve them simultaneously.

214 Medium

214 of 218

Analyzing +4 | -1

Assertion: Hydrostatic pressure is not a vector quantity.
Reason: Pressure is force divided by area, and force is a vector quantity.

View answer and explanation

Correct option: C

If assertion is true but reason is false

Option C (If assertion is true but reason is false) is correct because hydrostatic pressure is a scalar quantity, and while force is a vector, pressure itself is not.

Solution approach

Correct Answer + Core Reason: If assertion is true but reason is false. Hydrostatic pressure is a scalar quantity, not a vector.

Step-by-Step Solution:

Step 1: Analyze the Assertion: Hydrostatic pressure is indeed a scalar quantity. It has magnitude but no specific direction. It acts equally in all directions at a given point within the fluid.

Step 2: Analyze the Reason: While it's true that pressure is force divided by area ( $P = \frac{{F}}{{A}}$ ) and force is a vector, pressure itself is defined as a scalar. The direction of the force is normal to the surface, but the pressure is the magnitude of that force per unit area.

Step 3: Conclusion: The assertion is true, but the reason is false.

Why other options are wrong:
- Option A: The reason is false, so this option is incorrect.
- Option B: The reason is false, so this option is incorrect.
- Option D: The assertion is true, so this option is incorrect.

Key Concepts:
- Hydrostatic Pressure
- Scalar and Vector Quantities
- Definition of Pressure

Memory Aids:
- Pressure is a scalar; force is a vector.

Quick Tips:
- Distinguish between scalar and vector quantities.

215 Medium

215 of 218

Understanding +4 | -1

A drop of oil is placed on the surface of water then it will spread as a thin layer because

View answer and explanation

Correct option: B

surface tension of water is greater than that of oil

Option B (surface tension of water is greater than that of oil) is correct because the oil spreads to minimize the overall surface energy, which happens when the higher surface tension liquid (water) has a smaller surface area.

Solution approach

Correct Answer + Core Reason: surface tension of water is greater than that of oil. The oil spreads to reduce the overall surface energy.

Step-by-Step Solution:

Step 1: Define surface tension. Surface tension is the tendency of liquid surfaces to shrink into the minimum surface area possible.

Step 2: Consider the surface tensions of oil and water. If the surface tension of water is greater than that of oil, the water will try to minimize its surface area. When oil is placed on water, it spreads out to reduce the area of the water surface.

Step 3: Explain the spreading. The oil spreads as a thin layer because this arrangement minimizes the overall surface energy of the system. The higher surface tension of water pulls the oil outwards, causing it to spread.

Why other options are wrong:
- Option A: surface tension tends to give the oil a spherical surface - Surface tension would tend to minimize the oil's surface area, but the higher surface tension of water dominates.
- Option C: both oil and water have nearly equal surface tension - If the surface tensions were equal, there would be no strong driving force for the oil to spread.
- Option D: oil is lighter than water - While oil being lighter than water is true, it doesn't directly explain why it spreads as a thin layer. Density differences cause the oil to float, but surface tension differences cause it to spread.

Key Concepts:
- Surface Tension
- Minimization of Surface Energy

Memory Aids:
- Higher surface tension liquid will try to minimize its surface area.

Quick Tips:
- Consider the relative surface tensions when analyzing the behavior of liquids on surfaces.

216 Medium

216 of 218

Application +4 | -1

Two rain drops of same radii

'r'

, falling with terminal velocity

'v'

merge and form a bigger drops of radius

R

. The terminal velocity of the bigger drop is

View answer and explanation

Correct option: B

v\frac{{{R^2}}}{{{r^2}}}

Option B (

v\frac{{{R^2}}}{{{r^2}}}

) is correct because the terminal velocity is proportional to the square of the radius.

Solution approach

Correct Answer + Core Reason: $v\frac{{{R^2}}}{{{r^2}}}$ . Terminal velocity is proportional to the square of the radius.

Step-by-Step Solution:

Step 1: Recall the formula for terminal velocity:
$v = \frac{{2r^2(\rho - \sigma)g}}{{9\eta }}$ \nwhere $r$ is the radius, $\rho$ is the density of the raindrop, $\sigma$ is the density of air, $g$ is the acceleration due to gravity, and $\eta$ is the viscosity of air.

Step 2: Since the two raindrops merge, the volume of the bigger drop is the sum of the volumes of the two smaller drops:
$\frac{4}{3}\pi R^3 = \frac{4}{3}\pi r^3 + \frac{4}{3}\pi r^3 = 2 \times \frac{4}{3}\pi r^3$
$R^3 = 2r^3$
$R = r \times 2^{1/3}$

Step 3: The terminal velocity of the bigger drop is:
$v' = \frac{{2R^2(\rho - \sigma)g}}{{9\eta }}$

Step 4: Divide the terminal velocity of the bigger drop by the terminal velocity of the smaller drop:
$\frac{{v'}}{v} = \frac{{\frac{{2R^2(\rho - \sigma)g}}{{9\eta }}}}{{\frac{{2r^2(\rho - \sigma)g}}{{9\eta }}}} = \frac{{R^2}}{{r^2}}$
$v' = v\frac{{R^2}}{{r^2}}$

Why other options are wrong:
- Option A: $v\frac{R}{r}$ : This is incorrect because the terminal velocity is proportional to the square of the radius, not the radius itself.
- Option C: $v$ : This is incorrect because the terminal velocity changes when the radius changes.
- Option D: $2v$ : This is incorrect because the terminal velocity is not simply doubled.

Key Concepts:
- Terminal velocity
- Volume of a sphere

Memory Aids:
- Remember that terminal velocity is proportional to $r^2$ .

Quick Tips:
- Relate the radii using the conservation of volume.

217 Medium

217 of 218

Understanding +4 | -1

Two pieces of metal when immersed in a liquid have equal upthrust on them; then

View answer and explanation

Correct option: C

Both pieces must have equal volumes

Option C (Both pieces must have equal volumes) is correct because the upthrust force is directly proportional to the volume of the object submerged in the liquid, according to Archimedes' principle.

Solution approach

Correct Answer + Core Reason: Both pieces must have equal volumes. Equal upthrust implies equal volumes submerged.

Step-by-Step Solution:

Step 1: Recall Archimedes' principle: The upthrust on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

Step 2: Mathematically, upthrust $U = V \rho_L g$ , where $V$ is the volume of the object submerged, $\rho_L$ is the density of the liquid, and $g$ is the acceleration due to gravity.

Step 3: Since the upthrust is equal for both pieces, $V_1 \rho_L g = V_2 \rho_L g$ .

Step 4: This simplifies to $V_1 = V_2$ , meaning the volumes of the two pieces must be equal.

Why other options are wrong:
- Option A: Both pieces must have equal weights. This is incorrect. Upthrust depends on the volume of the object, not its weight directly. Objects of different densities can have the same volume and therefore the same upthrust, even if their weights are different.
- Option B: Both pieces must have equal densities. This is incorrect. Objects of different densities can have the same volume. Density is mass per unit volume, and upthrust depends on volume displaced.
- Option D: Both are floating to the same depth. This is incorrect. The depth to which an object floats depends on its density relative to the liquid's density. Equal upthrust does not imply equal floating depths.

Key Concepts:
- Archimedes' Principle
- Upthrust Force
- Volume and Density

Memory Aids:
- Upthrust = Weight of fluid displaced

Quick Tips:
- Upthrust depends on the volume submerged, not the weight of the object.

218 Medium

218 of 218

Analyzing +4 | -1

Assertion: The viscous force experienced by a steel ball moving in a liquid is less than that experienced by an aluminium ball of the same radius moving in the liquid with the same speed.
Reason: The density of steel is less than that of aluminium.

View answer and explanation

Correct option: D

If both assertion and reason are false

Option D is correct. The viscous force depends on the radius and speed, but not directly on the density of the ball. The density of steel is greater than that of aluminum.

Solution approach

Correct Answer + Core Reason: If both assertion and reason are false. Viscous force depends on radius and speed, and steel is denser than aluminum.

Step-by-Step Solution:

Step 1: Analyze the Assertion: According to Stokes' law, the viscous force (F) experienced by a sphere moving through a fluid is given by: $F = 6 \pi \eta r v$ , where $\eta$ is the viscosity of the fluid, r is the radius of the sphere, and v is the speed of the sphere. The formula does not directly depend on the density of the sphere. Since the radius and speed are the same for both the steel and aluminum balls, the viscous force will be the same, assuming they are moving in the same liquid. Therefore, the assertion is false.

Step 2: Analyze the Reason: The density of steel is greater than the density of aluminum. Therefore, the reason is also false.

Step 3: Conclusion: Both the assertion and the reason are false.

Why other options are wrong:
- Option A: Both the assertion and the reason are false, so this option is incorrect.
- Option B: Both the assertion and the reason are false, so this option is incorrect.
- Option C: The assertion is false, and the reason is also false, so this option is incorrect.

Key Concepts:
- Viscous force (Stokes' law): $F = 6 \pi \eta r v$
- Density

Memory Aids:
- Stokes' law: Viscous force depends on viscosity, radius, and velocity.

Quick Tips:
- Remember Stokes' law for viscous force.

Your Progress

Mechanical properties of fluids practice · Medium

Continue Your Practice

Your practice