Physics — Mixed Practice — Part 2: 40 MCQs with Explanations

1 kWh = 1000 W × 3600 s = 3,600,000 J = 3.6 × 10⁶ J.

Time period T = 2π√(l/g). If l becomes 4l, T becomes 2π√(4l/g) = 2 × 2π√(l/g) = 2T.

By Gauss's law and electrostatic shielding, electric field inside a conductor in electrostatic equilibrium is zero everywhere.

Resolving power ∝ 1/λ. Smaller wavelength gives better resolution (Rayleigh criterion).

Range R = u²sin2θ/g. For θ=45°, R₁ = u²/g. For θ=30°, R₂ = u²sin60°/g = (√3/2)u²/g = (√3/2)R.

Compton shift Δλ = λ' - λ = (h/m₀c)(1 - cosθ), where θ is scattering angle and m₀ is electron rest mass.

Leading zeros not significant. 0.00750 has 3 significant figures (7,5,0). Trailing zero after decimal is significant.

ω = 2π/T = 2π/(24×3600) ≈ 7.27 × 10^-5 rad/s.

When image at near point, magnifying power M = 1 + D/f. When image at infinity, M = D/f.

Common emitter amplifier produces 180° phase shift between input (base-emitter) and output (collector-emitter).

Second excited state is n=3. E_n = -13.6/n² eV. E₃ = -13.6/9 ≈ -1.51 eV.

L = μ₀N²A/l depends on N (turns), A (area), and l (length). Also depends on core material (μᵣ).

X-ray wavelengths range from about 0.01 nm to 10 nm (10^-11 to 10^-8 m), typically ~10^-10 m.

Number of neutrons N = A - Z = 235 - 92 = 143.

Minute hand completes 1 revolution in 1 hour; hour hand completes 1 revolution in 12 hours. ω ∝ 1/T, so ω_m/ω_h = T_h/T_m = 12/1.

Δx·Δp ≥ ħ/2 and ΔE·Δt ≥ ħ/2 are the two common forms of uncertainty principle.

Atomic number Z = number of protons = number of electrons in neutral atom.

Mass number A = number of protons (Z) + number of neutrons (N).

ΔE = E₂ - E₁ = -3.4 - (-13.6) = 10.2 eV.

r₁ = 0.529 Å ≈ 0.53 Å. r_n = n²r₁.

Ionization potential = energy required to remove electron from ground state = 13.6 eV, so 13.6 volts.

Shortest wavelength (highest energy) when electron falls from n=∞ to n=1: 1/λ = R(1/1² - 0) = R.

Longest wavelength (lowest energy) when electron falls from n=3 to n=2: 1/λ = R(1/2² - 1/3²) = 5R/36.

Binding energy = energy equivalent of mass defect = energy required to separate nucleus into its constituent protons and neutrons.

Chadwick discovered neutron by bombarding beryllium with alpha particles: ⁹Be + ⁴He → ¹²C + ¹n.

Penetrating power: γ > β > α. Alpha stopped by paper; beta by few mm Al; gamma requires thick lead/concrete.

In β⁻ decay: n → p + e⁻ + ν̄, so Z increases by 1, A unchanged. In β⁺ decay: p → n + e⁺ + ν, Z decreases by 1.

In α decay: parent → daughter + ⁴He, so Z decreases by 2, A decreases by 4.

Liquid drop model (Bohr & Wheeler) treats nucleus as charged liquid drop; explains fission as deformation overcoming surface tension.

Shell model (Mayer & Jensen) explains magic numbers (2,8,20,28,50,82,126) where nuclei exceptionally stable due to closed shells.

Ionization energy from n=2 = 0 - E₂ = 0 - (-3.4) = 3.4 eV.

Series limit (n=∞ → n=1): 1/λ = R(1 - 0) = R ⇒ λ = 1/R ≈ 91.2 nm.

E_n = -me⁴/(8ε₀²h²n²) ∝ -1/n².

E_n = -13.6 Z²/n² eV, so ionization energy from ground state = 13.6 Z² eV ∝ Z².

r_n = (0.53 Å)n²/Z. For He⁺ (Z=2), n=1: r₁ = 0.53/2 = 0.265 Å.

E_n = -13.6 Z²/n² eV. For Li²⁺ (Z=3), n=1: E₁ = -13.6 × 9 = -122.4 eV.

For Z=2 (He⁺), 1/λ = RZ²(1/1² - 1/2²) = 4R(3/4) = 3R ⇒ λ = 1/(3R) ≈ 30.4 nm.

Leading zeros (zeros to the left of the first non-zero digit) are not significant. The digits '3', '4', and the trailing zero after the decimal are significant, giving a total of 3 significant figures.

The dot product A·B = |A||B|cos θ. For the product to be zero, cos θ must be 0, which means θ = 90°. Therefore, the vectors are perpendicular (orthogonal).

The magnitude of the resultant R must satisfy |A - B| ≤ R ≤ |A + B|. Here, the range is from |10-5|=5 to |10+5|=15. A value of 4 lies outside this range and is impossible.