Physics · Properties of bulk matter · chapter 9 of 14

Class 11 Physics Chapter 9: Mechanical Properties of Fluids case study question with answers

One case-based question of the kind CBSE-pattern school exams ask: a passage and a table, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.

Case study · 4 marks

In a school laboratory, Ritika drops steel balls of different radii, one at a time, into a tall glass jar filled with castor oil at room temperature. Two rubber bands are tied round the jar, 20 cm apart, well below the oil surface. She times each ball between the bands and finds the time is the same however far above the top band she releases it, as long as the ball has already fallen a few centimetres in the oil before it reaches the top band. Her readings are given in the table.

radius of ball (mm)	1.0	2.0	3.0
steady speed (cm s⁻¹)	0.80	3.2	7.2

Part 1 · 1 mark

The readings show that the steady speed of a ball is proportional to

(a) its radius(b) the square of its radius(c) the cube of its radius(d) the inverse of its radius

Show answer

Answer: (b) the square of its radius

Doubling the radius multiplies the speed by 3.2/0.80 = 4 and tripling it by 7.2/0.80 = 9: v ∝ a², as v_t = 2a²(ρ − σ)g/(9η) predicts.

Part 2 · 1 mark

A ball of radius 1.5 mm of the same steel, in the same oil, would fall steadily at

(a) 1.2 cm s⁻¹(b) 2.0 cm s⁻¹(c) 1.8 cm s⁻¹(d) 2.7 cm s⁻¹

Show answer

Answer: (c) 1.8 cm s⁻¹

v ∝ a²: v = 0.80 × (1.5)² = 1.8 cm s⁻¹. Taking v ∝ a gives 1.2 cm s⁻¹; v ∝ a³ gives 2.7 cm s⁻¹.

Part 3 · 2 marks

Why must the ball fall a few centimetres in the oil before Ritika starts timing? Name the forces that balance during the timed fall.

Answer and marking scheme

The ball enters the oil slowly and accelerates; the viscous drag 6πηav grows with its speed until the drag and the buoyant force together equal its weight. Only then is the net force zero and the speed constant (the terminal velocity), which is what the timing measures. Balancing forces: weight downward; viscous drag and buoyant force upward.

ball accelerates at first; drag grows with speed until the speed is terminal (1)
weight balanced by viscous drag plus buoyant force (1)

Ritika repeats the experiment with the jar of oil warmed by 20 °C. Will the steady speeds be larger or smaller? Give the reason.

Answer and marking scheme

Larger. The viscosity of a liquid falls as its temperature rises, because its atoms become more mobile. Since v_t = 2a²(ρ − σ)g/(9η), a smaller η gives a larger terminal velocity.

speeds larger (1)
η of a liquid falls with temperature and v_t ∝ 1/η (1)

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