Physics Exam Preparation
Full explanation, worked examples & memory tricks in the app
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Full explanation, worked examples & memory tricks in the app
Every question in the paper gets a full exam-length answer in the app — organised by marks, the way a topper writes it.
Derive an expression for velocity of the particle for well of Death.
Velocity expression derived from energy conservation principles.
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State and prove principal of conservation of Angular momentum.
Angular momentum is conserved in an isolated system.
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Derive an Relation between surface tension & surface Energy.
Surface tension is the change in surface energy per unit area.
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Derive an expression for molar specific heat of a monoatomic gas at constant volume.
Molar specific heat at constant volume is \( C_v = rac{3R}{2} \).
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Derive an expression for differential eq'n. for Linear SHM.
Differential equation is \( rac{d^2x}{dt^2} + \omega^2 x = 0 \).
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Derive the decay law of radioactivity and state SI unit of 'activity'.
Decay law: \( N(t) = N_0 e^{-\lambda t} \), SI unit of activity is Becquerel (Bq).
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State Einstein's photoelectric eq'n. Hence, explain any two characteristics of photoelectric effect.
Einstein's equation: \( E = hf - \phi \); characteristics include threshold frequency and kinetic energy of emitted electrons.
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Derive an expression for electric potential due to a point charge.
Electric potential \( V = rac{kQ}{r} \).
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Obtain an expression for the electric intensity at a point outside a uniformly charged spherical shell.
Electric intensity outside a shell is \( E = rac{kQ}{r^2} \).
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Show that all harmonics are present in the case of an air column vibrating in a pipe open at both the end.
All harmonics are present due to boundary conditions at both ends.
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Derive an expression for equation of stationary wave on stretched string. Show that the distance between two successive nodes or antinodes is λ/2.
Distance between nodes is \( rac{\lambda}{2} \) derived from wave equation.
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Discuss analytically the composition of two linear SHMs having same period and along the same path. Obtain the expression for resultant amplitude.
Resultant amplitude is derived using phasor addition.
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Prove the Mayer's relation: Cp - Cv = R/J.
Mayer's relation connects heat capacities and gas constant.
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State differential eq'n of Linear SHM. Hence expression for acceleration, velocity and displacement of a particle performing SHM.
Differential equation: \( rac{d^2x}{dt^2} + \omega^2 x = 0 \); expressions for \( a, v, x \) derived.
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On the basis of kinetic theory of gases obtain an expression for pressure exerted by gas molecules enclosed in a container on its walls.
Pressure derived as \( P = rac{1}{3} rac{Nm}{V} \).
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Derive Laplace's law for spherical membrane of bubble due to surface tension.
Laplace's law relates pressure difference to surface tension and radius.
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Define: Angle of contact & write properties of Angle of contact.
Angle of contact is the angle between liquid surface and solid surface.
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Two tuning forks of frequencies 320Hz and 340 Hz are sounded together to produce sound wave. The velocity of sound in air is 326.4m/s. Calculate the difference in wavelength of these waves.
Difference in wavelength is calculated using \( \Delta \lambda = rac{v}{f_1} - rac{v}{f_2} \).
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(ii) A pipe open at both the ends has a fundamental frequency of 600Hz. The first overtone of a pipe closed at one end has the same frequency as the first overtone of the open pipe. How long are the two pipes? [Velocity of sound in air = 330m/s]
Length of pipes calculated using \( L = rac{v}{f} \).
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Differentiate between free vibration & force vibration.
Free vibration occurs without external force; forced vibration requires an external force.
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What is the effect of impurity on surface tension of liquid.
Impurities generally decrease surface tension.
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(i) State the law of length and the law of linear density for a vibrating string.
Law of length: frequency is inversely proportional to length; linear density affects frequency.
The full exam-length answer is in the app.
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