Mechanics & Motion — Part 2: 40 MCQs with Explanations

Magnetic force F = q(v × B). When v ⊥ B, force magnitude is qvB and direction is perpendicular to both v and B (given by right-hand rule).

For spring-mass system: T = 2π√(m/k).

Energy stored U = ½LI², analogous to ½CV² for capacitor and ½mv² for kinetic energy.

When lift accelerates upward with acceleration a, apparent weight = m(g+a) > mg (actual weight).

Speed of light (and all EM waves) in vacuum c = 2.998 × 10⁸ m/s ≈ 3 × 10⁸ m/s.

Work done W = qV. This is the definition of electric potential difference: V = W/q.

KEmax = hf - φ, where φ is work function. It depends on frequency f, not intensity.

For uniform density objects, center of mass coincides with geometric center. For triangle, it's the centroid (intersection of medians), located at 2/3 the distance from each vertex to opposite side.

Escape velocity vₑ = √(2GM/R), orbital velocity vₒ = √(GM/R). Therefore, vₑ/vₒ = √2.

Centripetal acceleration a = v²/r has constant magnitude but continuously changing direction (always toward center), so it's not constant.

Coulomb's law: F = kq₁q₂/r², describing electrostatic force between stationary point charges.

Earth completes 2π radians in 24 hours = 86400 s. ω = 2π/86400 ≈ 6.28/86400 ≈ 7.27 × 10⁻⁵ rad/s.

Elastic potential energy U = ½kx², where k is spring constant.

Hₘₐₓ = (v sinθ)²/2g = v²sin²θ/2g.

F = q(v × B) = qvB sinθ. When θ = 0° (parallel), sin0° = 0, so F = 0.

Orbital velocity near Earth's surface vₒ = √(gR) = √(9.8 × 6.4 × 10⁶) ≈ 7.9 km/s. Escape velocity = 11.2 km/s.

Linear velocity v = ω × r is tangential (perpendicular to radius), while angular velocity ω is axial (perpendicular to plane of rotation). So angle between ω and v is 90°.

Gravitational force acts radially inward while displacement is tangential (perpendicular). Since F ⊥ ds, work done dW = F·ds = 0.

Pascal's law: Pressure applied to confined fluid is transmitted undiminished to every portion of fluid and container walls. Hydraulic brakes use this principle to multiply force.

Photons are massless particles that always travel at speed of light c in vacuum. Their rest mass is zero.

Torque τ = pE sinθ. τ = 0 when sinθ = 0, i.e., θ = 0° or 180°. At θ = 0°, dipole is in stable equilibrium.

v ∝ √T (absolute temperature). v₂/v₁ = √(T₂/T₁). T₁ = 273 K, T₂ = 293 K. v₂ = 331 × √(293/273) ≈ 331 × 1.036 ≈ 343 m/s.

Work W = F·d·cosθ. When θ = 90°, cos90° = 0, so W = 0. Force perpendicular to displacement does no work.

Orbital velocity v₀ = √(GM/R) ≈ 7.9 km/s for low Earth orbit. Escape velocity is 11.2 km/s.

For elastic collision: v₁ = [(m₁-m₂)/(m₁+m₂)]u₁ = [(3-2)/(3+2)]×6 = (1/5)×6 = 1.2 m/s.

v ∝ √T. v₂/v₁ = √(T₂/T₁) = √(309/273) ≈ 1.064. v₂ ≈ 331 × 1.064 ≈ 352 m/s.

p = E/c = (4 × 1.6 × 10^-19)/(3 × 10^8) = 6.4 × 10^-19/3 × 10^8 = 2.13 × 10^-27 kg m/s.

Range R = u²sin2θ/g. Maximum when sin2θ = 1 ⇒ 2θ = 90° ⇒ θ = 45°.

Slope of v-t graph = dv/dt = acceleration. Area under v-t graph gives displacement.

First law (law of inertia) states that a body continues in its state of rest or uniform motion unless acted upon by external force.

Centripetal acceleration a = v²/r has constant magnitude but direction always toward center, so continuously changing direction.

Centripetal force is always perpendicular to displacement (tangential direction), so work done = F·d·cos90° = 0.

Original K = ½mv². New K' = ½(2m)(v/2)² = ½(2m)(v²/4) = ¼mv² = K/2.

F ∝ 1/r². If r becomes 2r, F becomes F/4.

Compton scattering (X-ray photons colliding with electrons) shows photons behave as particles with momentum p = h/λ.

v₁ = e²/2ε₀h ≈ 2.18 × 10^6 m/s ≈ c/137, where c = 3 × 10^8 m/s.

L = n(h/2π). For n=1, L = h/2π = ħ.

Mass defect Δm = (sum of masses of free nucleons) - (mass of nucleus) = (mass of reactants) - (mass of products) for reaction.

Neutrino (ν) postulated to conserve energy, momentum, and angular momentum in beta decay spectrum.

Nuclear force is short range (~1-3 fm), charge independent (same for p-p, n-n, p-n), spin dependent, and strongest fundamental force (at < 1 fm).