Physics — Mixed Practice — Part 3: 28 MCQs with Explanations

A unit vector has a magnitude of 1 and indicates direction. It is obtained by dividing a vector by its own magnitude: â = A / |A|.

Kepler's Third Law (Law of Periods) states that the square of the orbital period (T) of a planet is directly proportional to the cube of the semi-major axis (R) of its orbit. Mathematically, T² ∝ R³.

The time period of a simple pendulum is T = 2π√(L/g). T is proportional to √L. If L becomes 4L, then T becomes √4 = 2 times the original period.

Using Einstein's equation E = mc², the energy equivalent of 1 atomic mass unit (1 u = 1.66 × 10⁻²⁷ kg) is calculated to be about 931.5 mega-electronvolts (MeV).

Mass number (A) is the total number of protons and neutrons in the nucleus. A = Z + N = 6 + 8 = 14.

An intrinsic semiconductor is a pure semiconductor material without any significant dopant atoms present. Examples include pure silicon or germanium.

Doping is the intentional introduction of impurities into an intrinsic semiconductor to modulate its electrical properties. It creates either an excess of electrons (N-type) or holes (P-type).

The built-in potential (barrier potential) across the depletion layer of a PN junction is about 0.7 V for silicon diodes and about 0.3 V for germanium diodes.

The AND gate performs logical multiplication. Its output is true (1) only if all inputs are true (1). For example, for a 2-input AND gate, Y = A·B.

The NAND gate is the complement (NOT-AND) of the AND gate. Its output is the inverse of the AND gate output. It gives a LOW output only when all inputs are HIGH.

Modulus of elasticity (Young's modulus) is a measure of the stiffness of a material. Steel has a very high Young's modulus (around 2 × 10¹¹ N/m²), meaning it requires a large stress to produce a small strain.

According to the second law of thermodynamics, the total entropy of an isolated system can never decrease over time. It always increases for irreversible (spontaneous) processes and remains constant for reversible processes.

Silicon (Si) has an atomic number of 14. Its electronic configuration is 1s² 2s² 2p⁶ 3s² 3p². The outermost shell (n=3) contains 4 electrons (2 in the 3s and 2 in the 3p subshells).

Energy (in kWh) = Power (in kW) × Time (in hours). Power = 100 W = 0.1 kW. Time = 10 hours. Energy = 0.1 kW × 10 h = 1 kWh.

The magnitude of the cross product is |A × B| = |A||B| sin θ. This is zero when sin θ = 0, which occurs when θ = 0° (parallel) or θ = 180° (anti-parallel).

The binding energy per nucleon curve peaks at iron-56 (⁵⁶Fe). Nuclei around this mass number (A ≈ 50-60) are the most stable. Lighter and heavier nuclei have lower binding energy per nucleon.

Fringe spacing (β) in Young's double-slit experiment is given by β = λD/d, where λ is wavelength, D is screen distance, and d is slit separation. Therefore, β is inversely proportional to d (slit separation).

While atoms and molecules are the building blocks of matter we interact with, at a more fundamental level, protons and neutrons are made of quarks. According to the Standard Model, quarks and leptons are the fundamental particles.

Given |A × B| = |A||B| sin θ and A·B = |A||B| cos θ. For them to be equal, sin θ = cos θ. This occurs when tan θ = 1, i.e., when θ = 45° (or π/4 radians).

The second's hand completes one revolution (2π radians) in 60 seconds. Therefore, angular speed ω = θ/t = 2π / 60 = π/30 rad/s.

According to Bohr's postulates, the radius of the electron's orbit is given by r_n = n² a₀, where a₀ (0.529 Å) is the Bohr radius. Therefore, the radius is directly proportional to n².

Using s = ut + (1/2)gt², where u=0, s=20 m, g=10 m/s². Then 20 = (1/2)×10×t² => 20 = 5t² => t² = 4 => t = 2 s.

In the Bohr model, energy Eₙ = -13.6/n² eV. The ground state is n=1. The first excited state is n=2. Therefore, E₂ = -13.6/2² = -13.6/4 = -3.4 eV.

For isotropic materials, the coefficient of volume expansion is approximately three times the coefficient of linear expansion: β = 3α.

1 kWh is the energy consumed by a device of power 1 kW operating for 1 hour. It is a commercial unit of electrical energy. 1 kWh = 3.6 × 10⁶ J.

A seconds pendulum is defined as a pendulum whose time period is exactly 2 seconds. It takes 1 second for a swing from one extreme to the other and 1 second to return.

Beta-minus (β⁻) decay involves the emission of an electron and an antineutrino from the nucleus, which results from the conversion of a neutron into a proton.

In a neutral atom, the number of electrons is equal to the number of protons. The number of protons is given by the atomic number (Z). Therefore, if Z=17, there are 17 electrons.