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Questions and Answers
Which of the following is an incorrect relation for a diamagnetic material?
Which of the following is an incorrect relation for a diamagnetic material?
- -1 ≤ *x* < 0
- 0 ≤ *μr* < 1
- *μ* < *μ₀*
- 1 < *μr* < 1 + *ε* (correct)
In a non-uniform cross-sectional tube XY, if K₁ and K₂ are the kinetic energy per unit volume of the fluid at X and Y respectively, what is the relationship between K₁ and K₂?
In a non-uniform cross-sectional tube XY, if K₁ and K₂ are the kinetic energy per unit volume of the fluid at X and Y respectively, what is the relationship between K₁ and K₂?
- 2K₁ = K₂
- K₁ > K₂ (correct)
- K₁ = K₂
- K₁ < K₂
For a planet with 9 times the mass and 16 times the radius of Earth, what is the escape velocity of that planet compared to Earth's escape velocity?
For a planet with 9 times the mass and 16 times the radius of Earth, what is the escape velocity of that planet compared to Earth's escape velocity?
- 9*v*/4
- *v*/3
- 2*v*/3
- 3*v*/4 (correct)
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Study Notes
Diamagnetic Materials
- Diamagnetic materials have a relative permeability (μr) less than 1, i.e., 0 ≤ μr < 1
- The susceptibility (χ) of diamagnetic materials is between -1 and 0, i.e., -1 ≤ χ < 0
- The magnetic permeability (μ) of diamagnetic materials is less than the permeability of free space (μ₀), i.e., μ < μ₀
Ideal Fluids and Bernoulli's Principle
- Bernoulli's principle states that the sum of kinetic energy per unit volume, potential energy per unit volume, and pressure is constant
- Mathematically, this is represented as: ½ ρV² + ρgh + P = constant
- Applying Bernoulli's principle to a non-uniform cross-sectional tube, the kinetic energy per unit volume at the narrower end (K₁) is greater than at the wider end (K₂), i.e., K₁ > K₂
Escape Velocity
- The escape velocity from a planet's surface is given by a specific formula
- The escape velocity is dependent on the mass and radius of the planet
- If a planet has 9 times the mass and 16 times the radius of Earth, its escape velocity is 3v/4, where v is the escape velocity from Earth
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