NEETAceToday's NEET Daily

Viscosity by terminal velocity of a spherical body: NEET MCQs with answers

50 questions on this topic of Experimental Skills (NEET 2027 syllabus). Here are 12; tap one to see its answer and explanation.

Practise Experimental Skills freeAll Experimental Skills questions

Free with a Google sign-in; NEET Daily needs no sign-in at all.

easy

1. In an experiment to determine the viscosity of a liquid (density σ = 1.2 × 10³ kg m⁻³), a sphere of density ρ = 3.2 × 10³ kg m⁻³ attains a terminal speed of 0.20 m s⁻¹. If another sphere of identical size but density 2.2 × 10³ kg m⁻³ is dropped in the same liquid, its terminal speed will be:

  1. 0.05 m s⁻¹
  2. 0.15 m s⁻¹
  3. 0.10 m s⁻¹
  4. 0.25 m s⁻¹
Show answer and explanation

Answer: (C) 0.10 m s⁻¹

Terminal velocity v ∝ (ρ - σ). For the first ball, (ρ₁ - σ) = (3.2 - 1.2) × 10³ = 2.0 × 10³ kg m⁻³. For the second ball, (ρ₂ - σ) = (2.2 - 1.2) × 10³ = 1.0 × 10³ kg m⁻³. Hence, v₂ / v₁ = (1.0 / 2.0) = 0.5, giving v₂ = 0.5 × 0.20 m s⁻¹ = 0.10 m s⁻¹.

medium

2. A spherical lead ball falls through a column of a viscous liquid. At the exact instant when it attains terminal velocity, the net upward force exerted by the liquid on the ball is:

  1. equal to the true weight of the lead ball
  2. equal to the viscous drag only
  3. equal to the buoyant force only
  4. greater than the true weight of the lead ball
Show answer and explanation

Answer: (A) equal to the true weight of the lead ball

At terminal velocity, the acceleration of the sphere is zero, so the net force on the ball is zero. Therefore, the total upward force (buoyant force + viscous force) exerted by the liquid must be equal and opposite to the downward gravitational pull (true weight) of the ball.

hard

3. A metal sphere falling through a high-viscosity oil reaches 63.2% of its terminal speed in time τ (the characteristic time constant). If the radius of the sphere is r and its density is ρ, the characteristic time constant τ is directly proportional to:

  1. r / ρ
  2. r² / ρ
  3. ρ r²
  4. ρ / r
Show answer and explanation

Answer: (C) ρ r²

The equation of motion is m (dv/dt) = (m - m')g - 6πηrv. Dividing by m gives dv/dt + (6πηr/m)v = g_eff. The time constant τ is m / (6πηr). Since m = (4/3)πr³ρ, τ = [(4/3)πr³ρ] / (6πηr) = 2ρr² / (9η). Hence, τ is directly proportional to ρr².

medium

4. A spherical ball is dropped along the central vertical axis of a tall liquid column. If the ball is instead dropped very close to the inner wall of the cylindrical jar, the observed terminal speed will:

  1. increase because of reduced pressure near the wall
  2. first increase and then decrease to zero
  3. remain unchanged because terminal speed depends only on the liquid's bulk properties
  4. decrease due to increased viscous resistance from the wall
Show answer and explanation

Answer: (D) decrease due to increased viscous resistance from the wall

When the sphere moves close to the stationary wall, the velocity gradient in the fluid between the sphere and the wall becomes much steeper. This induces an additional retarding viscous drag (known as the wall effect), thereby decreasing the terminal speed.

easy

5. To observe uniform motion accurately in the falling sphere experiment, reference marks A and B are etched on the jar. The upper mark A should be located:

  1. Precisely at the liquid surface
  2. Near the bottom of the column to avoid surface effects
  3. Exactly at the midpoint of the liquid column
  4. Sufficiently below the surface to ensure the ball has attained terminal velocity
Show answer and explanation

Answer: (D) Sufficiently below the surface to ensure the ball has attained terminal velocity

The ball accelerates upon release due to gravity. To ensure that the timing interval measures a constant terminal velocity, the first timing mark A must be positioned far enough below the free surface so that the acceleration has reduced to zero.

hard

6. In a terminal velocity determination experiment, a spherical ball reaches 99% of its terminal velocity when the net acceleration of the ball is equal to:

  1. 0.99 g
  2. 0.01 g
  3. 0.01 g (1 - σ/ρ)
  4. 0.99 g (1 - σ/ρ)
Show answer and explanation

Answer: (C) 0.01 g (1 - σ/ρ)

The equation of motion is m a = m g (1 - σ/ρ) - 6πηrv. At terminal velocity v_t, 6πηrv_t = m g (1 - σ/ρ). When v = 0.99 v_t, m a = m g (1 - σ/ρ) - 0.99 m g (1 - σ/ρ) = 0.01 m g (1 - σ/ρ). Thus, the acceleration is a = 0.01 g (1 - σ/ρ).

easy

7. When performing the Stokes' law experiment to find the viscosity of a fluid, why is it essential to maintain a constant temperature of the liquid throughout the observations?

  1. Thermal expansion of the glass jar causes significant volume measurement errors.
  2. The density of the steel ball changes drastically with temperature.
  3. The viscosity of liquids varies strongly with temperature, decreasing sharply as temperature rises.
  4. Stokes' law is only derived for absolute zero temperature.
Show answer and explanation

Answer: (C) The viscosity of liquids varies strongly with temperature, decreasing sharply as temperature rises.

The viscosity of liquids decreases significantly with an increase in temperature due to weakening intermolecular forces. Even a small change in temperature during the experiment will alter η and lead to inconsistent terminal velocity readings.

easy

8. In the experiment to determine the coefficient of viscosity using Stokes' method, the wide glass jar containing the viscous liquid should have a sufficiently large diameter primarily to:

  1. minimize the loss of liquid due to splashing
  2. eliminate parallax error while viewing the reference marks
  3. minimize the boundary wall effect on the falling sphere
  4. prevent air bubbles from forming along the walls of the cylinder
Show answer and explanation

Answer: (C) minimize the boundary wall effect on the falling sphere

Stokes' law assumes that the sphere is moving through an infinitely extended fluid medium. A wide cylinder ensures that the walls are far enough from the falling sphere so that boundary wall corrections and retarding effects on the terminal speed are minimized.

medium

9. Small steel balls are used in this experiment so that:

  1. The flow remains streamline and Stokes' law applies
  2. The ball sinks faster
  3. Buoyancy becomes zero
  4. The liquid does not heat up
Show answer and explanation

Answer: (A) The flow remains streamline and Stokes' law applies

Stokes' law holds for small spheres moving slowly through a viscous liquid (streamline flow). Large or fast balls cause turbulence.

NCERT Class 11

easy

10. In an experiment to measure the coefficient of viscosity η of a highly viscous liquid by terminal velocity method, the formula used is η = [2r²(ρ - σ)g] / (9v). If the fractional uncertainty in measuring the radius r of the ball is 1.5% and the fractional uncertainty in measuring the terminal velocity v is 2.0%, while the densities ρ and σ are known precisely, the maximum percentage error in the calculated viscosity η is:

  1. 3.5%
  2. 4.0%
  3. 2.5%
  4. 5.0%
Show answer and explanation

Answer: (D) 5.0%

From the formula η ∝ r²/v, the maximum fractional error is Δη/η = 2(Δr/r) + (Δv/v). Substituting the given values: percentage error = 2(1.5%) + 2.0% = 3.0% + 2.0% = 5.0%.

medium

11. Which of the following velocity-time (v-t) graphs correctly illustrates the motion of a spherical ball released from rest from the free surface of a highly viscous liquid?

  1. A curve starting from origin whose slope continuously decreases and asymptotically approaches a constant non-zero value
  2. A straight line passing through the origin with a positive slope
  3. A curve starting from origin whose slope continuously increases to infinity
  4. A horizontal straight line at a constant non-zero velocity
Show answer and explanation

Answer: (A) A curve starting from origin whose slope continuously decreases and asymptotically approaches a constant non-zero value

As the sphere accelerates from rest, the upward viscous drag increases linearly with speed, causing the net downward force and thus acceleration (dv/dt, the slope of v-t curve) to decrease steadily to zero. The velocity asymptotically approaches the constant terminal velocity.

easy

12. In a terminal velocity experiment, a ball falls through a column of liquid. Which of the following graphs of total upward force (buoyant force plus viscous drag) versus time t correctly represents the motion until terminal velocity is attained?

  1. A curve starting from zero and increasing asymptotically to mg
  2. A horizontal straight line at a constant value equal to mg
  3. A curve starting from a positive non-zero value and decreasing to mg
  4. A curve starting from a positive non-zero value and increasing asymptotically to mg
Show answer and explanation

Answer: (D) A curve starting from a positive non-zero value and increasing asymptotically to mg

At t = 0, the sphere is dropped from rest, so the viscous force is zero, but the buoyant force is non-zero (equal to Vσg). As the velocity increases, the viscous drag 6πηrv increases until the total upward force equals the downward gravitational force mg, where net force becomes zero.

Keep going with Experimental Skills. All 954 questions with instant answers, your mistakes saved for revision and your accuracy by topic.
Start practising

Other topics in Experimental Skills