Mechanics & Motion — Part 1: 40 MCQs with Explanations

Conservative forces (like gravity, spring force) do work that depends only on initial and final positions, not on the path taken between them.

de Broglie wavelength λ = h/p, where h is Planck's constant and p is momentum.

Escape velocity v_e = √(2GM/R) ≈ 11.2 km/s for Earth.

Magnetic force F = q(v × B) = qvB sinθ. When velocity is parallel to field, θ = 0°, sin0° = 0, so force = 0.

KE = p²/2m. If p becomes 2p, KE becomes (2p)²/2m = 4p²/2m = 4 times original KE.

Using s = ut + ½at²: For first 4s: 40 = 4u + 8a. For total 8s: 100 = 8u + 32a. Solving: u = 5 m/s, a = 2.5 m/s².

K_max = hν - φ, depends only on frequency ν (not intensity). Intensity affects photocurrent magnitude only.

Parallel currents attract; antiparallel currents repel (Ampere's force law).

Gravitational potential energy U = -GMm/r is always negative for bound orbits.

Torque τ = pE sinθ. Maximum when sinθ = 1 ⇒ θ = 90°.

Orbital velocity v₀ = √(GM/R) ≈ 7.9 km/s for low Earth orbit.

If x = A sinωt, then a = -ω²x = ω²A sin(ωt + π). Phase difference = π (180°).

For elastic collision: v₁ = [(m₁-m₂)/(m₁+m₂)]u₁ = [(2-3)/(2+3)]×4 = (-1/5)×4 = -0.8 m/s.

de Broglie wavelength λ = h/p ∝ 1/p (inversely proportional to momentum).

Bohr's quantization: L = mvr = nħ = n(h/2π).

v ∝ √T. v₂/v₁ = √(T₂/T₁) = √(300/273) ≈ 1.048. v₂ ≈ 331 × 1.048 ≈ 347 m/s.

F/l = μ₀I₁I₂/2πr (attractive if currents parallel).

Electromagnetic induction: emf induced due to relative motion between conductor and magnetic field.

v_rms ∝ 1/√M. M_O₂/M_H₂ = 32/2 = 16. So v_H₂/v_O₂ = √16 = 4. Therefore v_H₂ = 4v.

Critical velocity v_c = (R_e η)/(ρD), depends on Reynolds number R_e, viscosity η, density ρ, and diameter D.

p = E/c = (3 × 1.6 × 10^-19)/(3 × 10^8) = 1.6 × 10^-27 kg m/s.

Phase velocity v_p = E/p = (γmc²)/(γmv) = c²/v > v (since v < c).

Uniform velocity means constant speed in a straight line. Since velocity is not changing, acceleration (rate of change of velocity) is zero.

Work done W = F·d·cosθ, where θ is the angle between force and displacement vectors. When θ = 90°, cos90° = 0, so W = 0.

The standard value of acceleration due to gravity at Earth's surface is 9.8 m/s² (often approximated as 10 m/s² in calculations).

Newton's first law states that a body at rest stays at rest and a body in motion continues in uniform motion unless acted upon by an external force. This property of matter to resist changes in motion is called inertia.

Kinetic energy KE = ½mv² = ½ × 2 × (3)² = ½ × 2 × 9 = 9 J.

Time period T = 2π√(l/g), where l is the length of pendulum and g is acceleration due to gravity. It is independent of mass and amplitude (for small angles).

de Broglie hypothesis: λ = h/p, where h is Planck's constant and p is momentum of the particle. This establishes wave-particle duality.

Range R = (v₀²sin2θ)/g. Maximum range occurs when sin2θ = 1, i.e., 2θ = 90°, so θ = 45°.

Centripetal force F = mv²/r, directed toward the center of the circle. It is required to keep the body in circular motion.

Conservation of linear momentum holds for an isolated system where net external force is zero. Internal forces do not affect the total momentum of the system.

Torque τ = pE sinθ, where p is dipole moment, E is electric field, and θ is angle between them. τ is maximum when sinθ = 1, i.e., θ = 90°.

Momentum p = mv = 5 × 4 = 20 kg·m/s.

Parallel conductors with currents in the same direction attract each other; with currents in opposite directions, they repel (Ampere's law).

Velocity of sound v = √(Y/ρ) for solids, where Y is Young's modulus and ρ is density. Solids have much higher elastic modulus compared to liquids and gases, so sound travels fastest in solids (steel: ~5000 m/s) compared to water (~1500 m/s) and air (~340 m/s). Sound cannot travel in vacuum.

Doppler effect for sound depends on velocities of source, observer, and medium relative to each other. Unlike light, sound requires a medium, so motion relative to medium matters.

Conservation of angular momentum: If net external torque acting on a system is zero, total angular momentum remains constant.

In SHM: x = A sin(ωt), v = Aω cos(ωt), a = -Aω² sin(ωt) = Aω² sin(ωt+π). So acceleration leads displacement by π radians (180°).

Maximum range Rₘₐₓ = v²/g (when θ = 45°).