NEET 2022 Physics Questions with Solutions

Explanation

Potential of a conducting sphere is given by: $$V = \frac{kQ}{R}$$ For equal charge, potential is inversely proportional to radius. Since $R_1 > R_2$, the smaller sphere has greater potential.

Explanation

Using Einstein’s photoelectric equation: $eV = h(\nu-\nu_0)$ For frequency $\nu$: $e\left(\frac{V_s}{2}\right)=h(\nu-\nu_0)$ ...(1) For frequency $\frac{\nu}{2}$: $eV_s=h\left(\frac{\nu}{2}-\nu_0\right)$ ...(2) Multiplying (1) by 2: $eV_s=2h(\nu-\nu_0)$ Equating with (2): $2(\nu-\nu_0)=\frac{\nu}{2}-\nu_0$ $2\nu-2\nu_0=\frac{\nu}{2}-\nu_0$ $\frac{3\nu}{2}=\nu_0$ Hence threshold frequency: $\boxed{\nu_0=\frac{3}{2}\nu}$ Therefore option (A) is correct.

Explanation

Speed of transverse wave on a stretched string: $$v = \sqrt{\frac{T}{\mu}}$$ If tension becomes double: $$v' = \sqrt{\frac{2T}{\mu}} = \sqrt{2}v$$ Therefore, $$v : v' = 1 : \sqrt{2}$$

Explanation

Typical wavelength ranges: - AM radio waves → $10^2\,m$ - Microwaves → $10^{-2}\,m$ - Infrared radiations → $10^{-4}\,m$ - X-rays → $10^{-10}\,m$ Hence the correct matching is: $$(a)-(ii), (b)-(iii), (c)-(iv), (d)-(i)$$

Explanation

For a disc: I(normal)=MR²/2 ⇒ k₁=R/√2; I(diameter)=MR²/4 ⇒ k₂=R/2. Hence ratio = (R/√2):(R/2)=√2:1.

Explanation

Using lens maker formula: 1/f=(μ−1)(1/R₁−1/R₂)=(0.5)(1/20−(−1/20))=1/20 cm⁻¹. Thus f=20 cm=0.2 m and P=1/f=+5 D.

Explanation

According to de Broglie relation, λ = h/p. Hence wavelength is inversely proportional to momentum, giving a decreasing hyperbolic curve. Therefore option (A) is correct.

Explanation

["The speed of electromagnetic waves in a medium is:","$$v=\\frac{1}{\\sqrt{\\mu\\varepsilon}}$$","For a material medium:","$$\\mu=\\mu_r\\mu_0, \\qquad \\varepsilon=\\varepsilon_r\\varepsilon_0$$","Substituting:","$$v=\\frac{1}{\\sqrt{\\mu_r\\mu_0\\varepsilon_r\\varepsilon_0}}$$","Using:","$$c=\\frac{1}{\\sqrt{\\mu_0\\varepsilon_0}}$$","Hence:","$$v=\\frac{c}{\\sqrt{\\varepsilon_r\\mu_r}}$$","Therefore, the correct answer is:","$$\\boxed{v=\\frac{c}{\\sqrt{\\varepsilon_r\\mu_r}}}$$"]

Explanation

In β⁺ decay, atomic number decreases by 1 while mass number remains unchanged. Hence ²²₁₁Na → ²²₁₀Ne + e⁺ + ν.

Explanation

For an ideal gas on a P–V diagram, the adiabatic curve is steeper than the isothermal curve because pressure decreases more rapidly during adiabatic expansion. Hence, among the given curves, process 2 represents the adiabatic process. Therefore, option (C) is correct.

Explanation

For a freely falling body under constant acceleration, distance covered in the nth second is: sₙ = u + a/2 (2n − 1) For free fall, u = 0 and a = g: sₙ ∝ (2n − 1) Thus, distances in successive seconds are: 1st : 2nd : 3rd : 4th = 1 : 3 : 5 : 7 Hence, option (D) is correct.

Explanation

Position of centre of mass: x = (m₂L)/(m₁ + m₂) = (20 × 10)/(10 + 20) = 200/30 = 20/3 m Hence, option (C) is correct.

Explanation

Energy radiated: E = Pt P = 100 kW = 10⁵ W t = 1 hour = 3600 s E = 10⁵ × 3600 = 36 × 10⁷ J Hence, option (B) is correct.

Explanation

Total opposing force: F = mg + friction = (2000 × 10) + 3000 = 23000 N Power: P = Fv = 23000 × 1.5 = 34500 W Hence, option (D) is correct.

Explanation

Excess pressure inside a soap bubble is: ΔP = 4T/r As the radius increases during expansion, excess pressure decreases. Hence pressure inside the bubble decreases. Therefore option (B) is correct.

Explanation

Statement I is correct because Biot–Savart law gives the contribution of an infinitesimal current element to magnetic field. Statement II is incorrect because charge is scalar while current element Idl is vector; the statement reverses these properties. Hence option (D) is correct.

Explanation

Initial momentum = 0. Masses are: 2m/5, 2m/5 and m/5. Momentum of two equal fragments: p₁ = (2m/5)v, p₂ = (2m/5)v Resultant momentum: p = √[(2m/5)v]² + [(2m/5)v]² = 2√2 mv/5 For third fragment: (m/5)V = 2√2 mv/5 V = 2√2v Hence option (D) is correct.

Explanation

A ball falling through viscous liquid attains terminal velocity. Velocity increases rapidly initially and gradually approaches a constant value. Curve B represents this behaviour. Hence option (C) is correct.

Explanation

Initial angular speed: ω₁ = 1200 × 2π/60 = 40π rad/s Final angular speed: ω₂ = 3120 × 2π/60 = 104π rad/s Angular acceleration: α = (ω₂ − ω₁)/t = (104π − 40π)/16 = 4π rad/s² Hence option (C) is correct.

Explanation

For alternating voltage: Vᵣₘₛ = V₀/√2 Therefore: V₀ = √2 Vᵣₘₛ Hence option (D) is correct.

Explanation

Magnetic permeability μ has dimensions: [μ] = [MLT⁻²A⁻²] Hence option (D), magnetic permeability, is correct.

Explanation

Velocity equals slope of displacement-time graph. v₁/v₂ = tan30°/tan45° = (1/√3)/1 = 1 : √3 Hence option (A) is correct.

Explanation

In circuits (a) and (c), the two identical p-n junctions experience equal potential drops due to symmetric biasing conditions. Hence the correct answer is option (A).

Explanation

Electric field lines are always perpendicular to equipotential surfaces because no work is done in moving along an equipotential surface. Hence, the angle between them is 90°. Therefore option (D) is correct.

Explanation

Plane angle and solid angle are dimensionless quantities but have SI units: radian and steradian respectively. Therefore, they have units but no dimensions. Hence option (B) is correct.

Explanation

Fringe width in YDSE: β ∝ λ Number of fringes in a fixed screen length: N ∝ 1/λ Thus, N₂/N₁ = λ₁/λ₂ N₂/8 = 600/400 N₂ = 12 Hence option (A) is correct.

Explanation

Using Snell's law: sin i / sin r = μ sin 60° / sin r = √3 (√3/2)/sin r = √3 sin r = 1/2 r = 30° Reflected angle = 60° Angle between reflected and refracted rays: = 180° − (60° + 30°) = 90° Hence option (D) is correct.

Explanation

For half-wave rectification, output frequency equals input frequency: f_output = f_input Thus: f_output = 60 Hz Hence option (D) is correct.

Explanation

Gravitational field intensity: g = F/m = 3/(0.06) = 50 N/kg Hence option (C) is correct.

Explanation

Magnetic flux: Φ = BA cosθ Area = 1 × 1 = 1 m² Since plane is perpendicular to field, θ = 0° Φ = 0.5 × 1 × 1 = 0.5 Wb Hence option (C) is correct.

Explanation

For hydrogen atom: Eₙ ∝ -1/n² First excited state: n = 2 Second excited state: n = 3 T₁:T₂ = (1/2²):(1/3²) = 1/4 : 1/9 = 9 : 4 Hence option (A) is correct.

Explanation

Magnetic field inside long solenoid: B = μ₀nI n = 100 turns/mm = 10⁵ turns/m μ₀ = 4π × 10⁻⁷ Tm/A I = 1 A B = 4π × 10⁻⁷ × 10⁵ × 1 = 4π × 10⁻² ≈ 12.56 × 10⁻² T Hence option (C) is correct.

Explanation

Time period of a pendulum: T ∝ √L Therefore: T₁/T₂ = √121/√100 = 11/10 For the pendulums to return to the mean position in the same phase: n₁T₁ = n₂T₂ Minimum integers satisfying: n₁/n₂ = 10/11 Thus, the shorter pendulum completes 11 vibrations. Hence option (B) is correct.

Explanation

Mass of water: m = 4.5 kg = 4500 g Number of moles: n = 4500/18 = 250 mol At STP, 1 mol ideal gas occupies 22.4 × 10⁻³ m³. Thus: V = 250 × 22.4 × 10⁻³ = 5.6 m³ Hence option (A) is correct.

Explanation

Refractive index is inversely proportional to speed: n₁/n₂ = v₂/v₁ Critical angle: sin C = n₂/n₁ = v₁/v₂ = (1.5 × 10⁸)/(2.0 × 10⁸) = 0.75 Thus: C = sin⁻¹(0.750) Hence option (C) is correct.

Explanation

Dimensions: G → [M⁻¹L³T⁻²] Potential energy → [ML²T⁻²] Potential → [L²T⁻²] Intensity → [LT⁻²] Thus matching: (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii) Hence option (C) is correct.

Explanation

Angular frequency of source: ω = 100 rad/s ν = ω/2π = 100/2π = 50/π Hz Resonance frequency: ν₀ = 1/(2π√LC) = 1/[2π√(10×10⁻⁵)] = 50/π Hz Hence: ν₀ = ν = 50/π Hz Therefore option (C) is correct.

Explanation

Angle with horizontal: θ = 30° At highest point, vertical velocity = 0. Remaining horizontal velocity: v = u cos30° = 10 × √3/2 = 5√3 ms⁻¹ Hence option (C) is correct.

Explanation

Extension in a coil spring depends on the shear modulus (modulus of rigidity) of the material, so Assertion (A) is true. Copper has lower tensile strength than steel, hence Reason (R) is false. Therefore option (D) is correct.

Explanation

Evaluating the logic gates in sequence gives output values: A B → C 00 → 1 01 → 0 10 → 1 11 → 0 Hence option (D) is correct.

Explanation

Nuclear radius: R ∝ A^(1/3) Thus: R₁/R₂ = (125/64)^(1/3) = 5/4 Hence the ratio is 5 : 4. Therefore option (D) is correct.

Explanation

Area = length × breadth = 55.3 × 25 = 1382.5 m² The least number of significant figures is 2 (from 25). Thus rounded value: = 1.4 × 10³ m² = 14 × 10² m² Hence option (A) is correct.

Explanation

Maximum induced emf: Eₘ = NBAω N = 1000, B = 2 × 10⁻⁵ T, A = π(10)² = 100π m², ω = 2 rad/s Eₘ = 1000 × 2×10⁻⁵ × 100π × 2 = 4π V Maximum current: Iₘ = Eₘ/R = 4π/12.56 ≈ 1 A Hence option (D) is correct.

Explanation

The arrangement forms an electric dipole. The electric field due to a dipole at a distant point varies as: E ∝ 1/R³ Hence option (C) is correct.

Explanation

Initial energy: U = ½CV² = ½ × 900×10⁻¹² × (100)² = 4.5 × 10⁻⁶ J After connecting to identical uncharged capacitor, charge redistributes equally and energy becomes half: U' = U/2 = 2.25 × 10⁻⁶ J Hence option (D) is correct.

Explanation

For hydrogen-like species: rₙ ∝ n²/Z Given: For He+ (Z = 2), n = 2: r₂ = 105.8 pm For Li2+ (Z = 3), n = 3: r = 105.8 × (3²/3)/(2²/2) = 105.8 × (3/2) = 158.7 pm Hence option (B) is correct.