Unit 7: Properties of Solids and Liquids — Online MCQ Test
PHYSICS · JEE MAINS · JEE
Practice Unit 7: Properties of Solids and Liquids with a free chapter-wise online MCQ test.
This chapter covers: Elastic behaviour stress-strain relationship Hooke's Law Young's modulus bulk modulus and modulus of rigidity. Syllabus for JEE (Main) - 2026 Pressure due to a fluid column Pascal'....
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Unit 7: Properties of Solids and Liquids — Important Questions & Answers
A spherical body of radius r and density σ falls freely through a viscous liquid having density ρ and viscosity η and attains a terminal velocity v0. Estimated maximum error in the quantity η is: (Ignore errors associated with σ, ρ, and g)
- A. Δη/η = Δr/r - Δv0/v0 * 2
- B. Δη/η = 2Δr/r + Δv0/v0
- C. Δη/η = [Δr/r + Δv0/v0] * 2
- D. Δη/η = [Δr/r - Δv0/v0] * 2
Answer: B. Δη/η = 2Δr/r + Δv0/v0
From Stokes' Law, terminal velocity v0 = [2r²g(σ - ρ)] / 9η. Rearranging for η: η = [2r²g(σ - ρ)] / 9v0. Ignoring errors in constants/densities, η ∝ r²/v0. Using error propagation, Δη/η = 2(Δr/r) + Δv0/v0.
From Stokes' Law, terminal velocity v0 = [2r²g(σ - ρ)] / 9η. Rearranging for η: η = [2r²g(σ - ρ)] / 9v0. Ignoring errors in constants/densities, η ∝ r²/v0. Using error propagation, Δη/η = 2(Δr/r) + Δv0/v0.
Surface tension of two liquids (having same densities), T1 and T2, are measured using capillary rise method utilizing two tubes with inner radii r1 and r2 where r1 > r2. The measured liquid heights are h1 and h2 respectively. The heights h1 and h2 and surface tensions T1 and T2 satisfy the relation:
- A. h1 < h2 and T1 = T2
- B. h1 = h2 and T1 = T2
- C. h1 > h2 and T1 = T2
- D. h1 > h2 and T1 < T2
Answer: A. h1 < h2 and T1 = T2
Capillary rise height h = 2T/(rρg). Thus h ∝ 1/r. Since r1 > r2, it follows that h1 < h2. Assuming the same liquid properties, T1 = T2.
Capillary rise height h = 2T/(rρg). Thus h ∝ 1/r. Since r1 > r2, it follows that h1 < h2. Assuming the same liquid properties, T1 = T2.
The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm/s. The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be ____ cm/s.
- A. 5
- B. 10
- C. 15
- D. 20
Answer: A. 5
Terminal velocity vT is proportional to the square of the radius (vT proportional to r^2). Therefore, v2/v1 = (r2/r1)^2 = (3/6)^2 = (1/2)^2 = 1/4. v2 = 20 * (1/4) = 5 cm/s.
Terminal velocity vT is proportional to the square of the radius (vT proportional to r^2). Therefore, v2/v1 = (r2/r1)^2 = (3/6)^2 = (1/2)^2 = 1/4. v2 = 20 * (1/4) = 5 cm/s.
When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height h. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by 1% each, then the height of the liquid in the tube will change by ____ %.
- A. -1
- B. +3
- C. -3
- D. +1
Answer: D. +1
Formula is h = (2T cos θ) / (ρ g r). Taking log and differentiating: Δh/h = ΔT/T - Δρ/ρ - Δr/r. Since T, ρ, and r all decrease by 1% (-1%), Δh/h = (-1%) - (-1%) - (-1%) = -1 + 1 + 1 = +1%.
Formula is h = (2T cos θ) / (ρ g r). Taking log and differentiating: Δh/h = ΔT/T - Δρ/ρ - Δr/r. Since T, ρ, and r all decrease by 1% (-1%), Δh/h = (-1%) - (-1%) - (-1%) = -1 + 1 + 1 = +1%.
Given below are two statements : Statement I : Pressure in a reservoir of water is same at all points at the same level of water. Statement II : The pressure applied to enclosed water is transmitted in all directions equally. In the light of the above statements, choose the correct answer from the options given below :
- A. Both Statement I and Statement II are true
- B. Both Statement I and Statement II are false
- C. Statement I is true but Statement II is false
- D. Statement I is false but Statement II is true
Answer: A. Both Statement I and Statement II are true
Statement I is true because in a fluid at rest, pressure depends only on depth, so all points at the same horizontal level have the same pressure. Statement II is also true; it is Pascal's law, which says that pressure applied to an enclosed fluid is transmitted equally in all directions. Therefore, both statements are true.
Statement I is true because in a fluid at rest, pressure depends only on depth, so all points at the same horizontal level have the same pressure. Statement II is also true; it is Pascal's law, which says that pressure applied to an enclosed fluid is transmitted equally in all directions. Therefore, both statements are true.