The Multiple Choice Questions with solutions are divided into three categories:
Question Bank
Formula-Based Questions
SI Units Asked
Q–2: The SI unit of Electric Field is:
Explanation
Correct answer: Volt/meter (same as Newton per coulomb).
Derived Formulas Asked
Q–1: Two spheres A and B of radius ‘a’ and ‘b’ are at same electric potential. The ratio of surface charge densities is:
Explanation
Correct answer: b/a, using V = σR/ε₀.
Q–1: Two spheres A and B of radius ‘a’ and ‘b’ are at same electric potential. The ratio of surface charge densities is:
Explanation
Correct answer: b/a, using V = σR/ε₀.
Simple/Direct Formulas Asked
Q–1: Which of the following is the correct mathematical statement of Gauss’s Law?
Explanation
Correct answer: ∮E·dA = Q/ε₀. Gauss’s Law relates the total electric flux through a closed surface to the charge enclosed.
Q–2: Coulomb’s force law in vector form is:
Explanation
Correct answer: F = (1/4πε₀)(q₁q₂/r²) r̂. This is Coulomb’s inverse-square law in vector form.
Theory-Based Questions
Figure-based Conceptual Reasoning
Numerical-Based Questions
Q–1: How much heat energy should be added to a mixture of 10 g of hydrogen and 40 g of helium to change the temp. by 50∘C kept in a closed vessel? Given R = 2 cal/mole K
Explanation
Correct answer: 2750 cal (Vm or N·m²/C). check out the animation for this!
To calculate the heat energy that should be added to a mixture of hydrogen and helium to raise its temperature by 50°C in a closed vessel, the following steps are taken:
1. Determine the number of moles of each gas:
The molar mass of hydrogen (H₂) is approximately 2 g/mol .
The number of moles of hydrogen is: 10 g / 2 g/mol = 5 moles.
The molar mass of helium (He) is approximately 4 g/mol .
The number of moles of helium is: 40 g / 4 g/mol = 10 moles.
2. Identify the molar specific heat at constant volume (Cv) for each gas:
Since the gas is in a closed vessel, the volume is constant, and we use the molar specific heat at constant volume.
Hydrogen is a diatomic gas, so its molar specific heat at constant volume (Cv) is (5/2)R.
Given R = 2 cal/mol K, the Cv for hydrogen is (5/2) * 2 = 5 cal/mol K.
Helium is a monatomic gas, and its molar specific heat at constant volume (Cv) is (3/2)R.
The Cv for helium is (3/2) * 2 = 3 cal/mol K.
3. Calculate the heat energy required for each gas:
The formula to calculate the heat energy (ΔQ) required to change the temperature of a gas at constant volume is ΔQ = n * Cv * ΔT, where ‘n’ is the number of moles, ‘Cv’ is the molar specific heat at constant volume, and ‘ΔT’ is the change in temperature.
For hydrogen: ΔQ_H₂ = 5 moles * 5 cal/mol K * 50 K = 1250 cal.
For helium: ΔQ_He = 10 moles * 3 cal/mol K * 50 K = 1500 cal.
4. Calculate the total heat energy:
The total heat energy required is the sum of the heat energy required for each gas.
Total ΔQ = ΔQ_H₂ + ΔQ_He = 1250 cal + 1500 cal = 2750 cal.
Therefore, 2750 calories of heat energy should be added to the mixture to increase its temperature by 50°C.
Figure-based Numericals
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