#hsc 12th
- Using analytical method, obtain an expression for the fringe width of two interfering waves. Answer: Fringe width X = λ D/d Let S₁ and S₂ be two coherent monochromatic sources of wavelength λ , separated by distance d , and let the s... 1
- Name an instrument for measurement of e.m.f. of a cell. Answer: Potentiometer. At the null point a potentiometer draws no current from the cell, so it measures the true e.m.f. (a voltmeter draws s... 1
- Which property of bar magnet is used in navigation? Answer: The directive property. A freely suspended bar magnet always comes to rest along the geographic north–south direction. This is used... 1
- What is beta plus decay? Answer: Beta plus ( β^+ ) decay is the radioactive decay in which a proton in the nucleus changes into a neutron, emitting a positron and a... 1
- Define second’s pendulum. Answer: A second’s pendulum is a simple pendulum whose period is two seconds. It takes one second to swing from one extreme to the other. It... 1
- Calculate the magnitude of force experienced by a stationary charge exposed to uniform magnetic field. Answer: Zero. The magnetic force on a charge is F = qvBsinθ . For a stationary charge v = 0 , so F = q(0)Bsinθ = 0 . 1
- In Young’s double slit experiment, width of the two slits are in the ratio 25 : 1. Calculate the ratio of amplitudes. Answer: a₁ : a₂ = 5 : 1 Intensity of light from a slit is proportional to its width, and intensity ∝ (amplitude) ² . So a₁/a₂ = √(I₁/I₂) = √... 1
- If the tension in sonometer wire is increased by 21%, compare the initial frequency with the later. Answer: n₁ : n₂ = 10 : 11 For a sonometer wire n = 1/2l√(T/m) , so n ∝ √(T) . New tension T₂ = 1.21 T₁ : n₁/n₂ = √(T₁/1.21 T₁) = 1/1.1 = 10/... 1
- What are Eddy currents? State its two applications. Answer: Eddy currents are the circulating induced currents set up in the body of a conductor when the magnetic flux through it changes. Appl... 1
- State any two sources of error in meter bridge experiment. Explain how they can be minimised. Answer: (1) End resistance/contact resistance at the ends of the wire — minimised by interchanging the two resistances and taking the mean,... 1
- Draw a ray diagram showing position of virtual sources and region of interference in biprism experiment. Answer: The biprism splits the wavefront from the slit S into two parts which appear to come from two virtual coherent sources S₁ and S₂; in... 1
- Derive an expression for radius of nth Bohr orbit. Answer: r_n = ε₀ h² n²/π m Z e² (for hydrogen Z = 1 ). Consider an electron of mass m , charge e moving with speed v_n in the n th circular... 1
- A ceiling fan has moment of inertia of 2 kg m\(^2\). It attains maximum frequency of 60 r.p.m. in \(2\pi\) seconds. Calculate its power rating. Answer: P = 4π ≈ 12.57 W Given: I = 2 kg m ² , n = 60 r.p.m. = 1 r.p.s., t = 2π s, starting from rest. Maximum angular speed: ω = 2π n = 2π... 1
- An electric dipole consists of two unlike charges of magnitude \(2 \times 10^{-6}\) C each and separated by 4 cm. The dipole is placed in an external electric field of \(10^5\) N/C. Calculate the work done by an external agent to turn the dipole thro… Answer: W = 0.016 J Dipole moment p = q(2l) = 2×10⁻⁶ × 0.04 = 8×10⁻⁸ C m. Work done in rotating the dipole from θ₁ to θ₂ : W = pE(cosθ₁ - co... 1
- Derive an expression for the magnetic field produced by a current in a circular arc of a wire using Biot-Savart law. Answer: At the centre of an arc of radius R subtending angle φ (in radian), B = μ₀ I φ/4π R . Consider a wire bent into a circular arc of ra... 1
- State advantages and disadvantages of photodiode. Answer: Advantages — quick response, low noise, low cost and small size, can work at high frequency (long life, no high voltage needed). Dis... 1
- Distinguish between harmonics and overtones. [Any Two points] Answer: HarmonicsOvertones 1. Harmonics are frequencies that are integral multiples of the fundamental frequency.1. Overtones are the freque... 1
- A steel ball with radius 0.3 mm is falling with velocity of 2 m/s through a tube filled with glycerine. Calculate viscous force acting on the steel ball. [ Given : \(\eta_{\text{glycerine}} = 0.833\) N s/m\(^2\) ] Answer: F ≈ 9.42×10⁻³ N By Stokes’ law, F = 6πη r v . r = 0.3 mm = 3×10⁻⁴ m, v = 2 m/s, η = 0.833 N s/m ² . F = 6 × 3.142 × 0.833 × 3×10⁻⁴ ×... 1
- Calculate the temperature at which the average kinetic energy of a molecule of a gas will be same as that of an electron accelerated through 1 volt. [ Given: \(k_B = 1.4 \times 10^{-23}\) J/K, \(e = 1.6 \times 10^{-19}\) C ] Answer: T ≈ 7.62×10³ K (about 7619 K) Energy gained by an electron accelerated through 1 V: E = eV = 1.6×10⁻¹⁹ J. Average K.E. of a gas mole... 1
- An inductor of inductance 200 mH is connected to an A.C. source of peak e.m.f. 220 V and frequency 50 Hz. Calculate the peak current in the circuit. Answer: i₀ ≈ 3.5 A Inductive reactance X_L = 2π f L = 2 × 3.142 × 50 × 0.2 = 62.84\ Ω . i₀ = e₀/X_L = 220/62.84 ≈ 3.50\ A 1
- In thermodynamics, define : (a) Mechanical equilibrium (b) Chemical equilibrium (c) Thermal equilibrium Answer: (a) Mechanical equilibrium: A system is in mechanical equilibrium when there are no unbalanced forces within it or between it and it... 1
- Derive an expression for resonant frequency of series resonant circuit. Answer: f_r = 1/2π√(LC) In a series LCR circuit connected to an a.c. source e = e₀sinω t , the impedance is Z = √(R² + (X_L - X_C)²),qquad X... 1
- Obtain an expression for period of a bar magnet vibrating in a uniform magnetic field and performing angular S.H.M. Answer: T = 2π√(I/mB) Consider a bar magnet of magnetic moment m and moment of inertia I (about the axis of suspension) suspended in a unifo... 1
- Define magnetization. State its S.I. unit and dimensions. What is the relation between permeability and magnetic susceptibility? Answer: Magnetization is the net magnetic dipole moment per unit volume of a material; S.I. unit A/m; dimensions [L⁻¹A] i.e. [M⁰L⁻¹T⁰A¹] ; μ... 1