Physics Numerical Problems

phy-1109 PHY-1109 Physics

NUMERICAL PROBLEMS (PYQS 2016–2024)

I. OSCILLATIONS AND MECHANICAL WAVES

Subtopic	Question (Numerical Input/Calculation Required)	Year(s)
SHM Superposition	Two SHM’s acting simultaneously on a particle are given by the equation. $Y_1=2\sin (\omega t+\pi /4)$ and $Y_2=3\sin (\omega t+\pi /3)$. Calculate (i) amplitude (ii) phase constant (iii) time period of the resultant vibration.	2016
SHM Superposition	Two SHM $y_1=5\sin (\omega t+\pi /2)$ , $y_2=6\sin (\omega t+\pi /3)$. Determine (i) amplitude, (ii) phase constant, (iii) time period of the resultant vibration.	2024, 2024(becm)
SHM Calculation	A SHM is presented by $y=12\sin (6t-\pi /3)$. Calculate the frequency, epoch, maximum displacement, velocity and acceleration at $t=0$ and $t=6$ seconds.	2018
SHM Calculation	Body vibrating with SHM of amplitude 15 cm and frequency 4 Hz. Determine maximum velocity/acceleration/speed when body is 9 cm from equilibrium.	2021
Work Done (Forced Oscillation)	Force $F=5\sin (\pi t)$, displacement $y=0.50\sin (\pi t-\pi /4)$. Calculate the work done in 30 seconds and in 5 minutes.	2019
Work Done (Forced Oscillation)	Force $F=25\sin (\pi t/10)$, displacement $Y=0.5\sin (\pi t/10-\pi /4)$. Calculate the work done by the excitation force in (i) 30 seconds and (ii) 5 minutes.	2020
Work Done (Forced Oscillation)	Force $F=0.5\sin (2t)$, displacement $Y=0.5\sin (2t-\pi /2)$. Calculate the work done by the excitation force in (i) 12 minutes and (ii) one day.	2022
Wave Parameters	Wave along a string $y=0.02\sin (30t-4x)$. Find amplitude, frequency, speed and wavelength.	2018
Stationary Waves	Stationary wave $y=0.8\sin (0.32x)\cos (16t)$. What are amplitude and velocity of individual waves?.	2019
Damped Oscillation	Under damped harmonic oscillator: amplitude reduced to 1/10th after 100 oscillations. T=1.25 sec. Calculate (i) damping constant and relaxation time, (ii) amplitude without damping.	2017, 2020
Resonance (LCR)	Deduce the frequency and quality factor for a circuit with $L=2$ mH, $C=50\mu F$ , and $R=2$ ohms.	2019
Resonance (LCR)	Calculate the frequency and quality factor for a circuit with $L=5.2$ mH, $C=5\mu F$ , and $R=0.35$ ohm.	2024
Forced Oscillation	Particle mass 2 gm, damping force $8\text{ dyne-sec/cm}$. Periodic force $250\sin (2t)$ dyne applied. Determine frequency for displacement resonance and velocity resonance.	2021
Damping Check (LCR)	Find whether the discharge of a condenser for the following inductive circuit is oscillatory: $C=0.1\mu F,L=10$ mH, $R=210$ ohms. If oscillatory, calculate its frequency.	2023
Forced Oscillation	Harmonic oscillator Q=12 subjected to sinusoidal force. Calculate (i) amplitude of forced oscillation (ii) angle $\varphi$ by which it will be out of phase with the driving force.	2024(becm)
Doppler’s Effect	Two aeroplanes pass each other… calculate the frequencies of the notes heard in the other aeroplane (i) before and (ii) after they have passed each other.	2016
Doppler’s Effect	Apparent frequency of whistle changes in ratio 6:5 as engine passes stationary observer. Calculate $V_{engine}$.	2022
Acoustics	Calculate the increase in the acoustic intensity level when the sound is doubled.	2017
Acoustics	Calculate the change in intensity level when the intensity of sound increases 100 times its original intensity.	2023
Acoustic Intensity	Calculate the (i) acoustic intensity (ii) acoustic pressure of a plane, acoustic wave in air of intensity level of 80 decibels reference to $10^{-12}{\text{ watt/m}}^2$.	2016, 2022
Acoustic Intensity	Calculate acoustic intensity and acoustic pressure of a plane acoustic wave in air of intensity level of 100 dB reference to $10^{-12}{\text{ watt/m}}^2$.	2021
Sound Energy Flow	Sound source $f=250$ Hz, $A=0.40$ cm. Determine rate of flow of energy per square cm.	2024(becm)
Sound Energy Flow	Sound source $f=256$ Hz, $A=5\times 10^{-5}$ m. Calculate the flow of energy across a square meter per second.	2024
Reverberation	Room volume 750 m ${}^3$. Calculate average absorption coefficient and reverberation time given coefficients for walls, floor, and ceiling.	2024(becm)
Reverberation	Room $6\times 5\times 4$ meters. Calculate (i) mean free path of the sound wave, (ii) number of reflection made per second by the sound wave.	2023

II. OPTICS

Subtopic	Question (Numerical Input/Calculation Required)	Year(s)
Young’s Double Slit	Young’s double slit experiment: slit separation 1.9 mm, fringe spacing 0.31 mm at 1 m distance. Calculate $\lambda$.	2016
Young’s Double Slit	Two coherent sources 0.22 mm apart. Screen 70 cm away. 4th bright fringe is 10 mm from central fringe. Calculate $\lambda$.	2017
Young’s Double Slit	Light of wavelength $5500\text{A˚}$ incident on double slit. Fringe separation $1$ cm on screen $200$ cm away. Calculate (i) slit separation and (ii) fringe width.	2020
Fresnel’s Bi-prism	Bi-prism calculation: $\lambda =5890\text{A˚}$, fringes 0.2 mm apart, $D=175$ cm. $\mu =1.5$. Prism is 5 cm from slit. Calculate angle at vertex.	2019
Fresnel’s Bi-prism	Bi-prism is placed 6 cm from slit. Fringes $0.05$ cm wide. $D=75$ cm. Find width of fringes observed if an eyepiece placed at 75 cm from the bi-prism.	2023
Newton’s Rings	Newton’s rings experiment: diameter of 5th ring was 0.336 cm, 15th ring=0.590 cm. Find the radius of curvature of the plano-convex lens, if the wavelength of the light used is $5890\text{A˚}$.	2016, 2022
Newton’s Rings	Newton’s ring calculation: diameter of 15th ring 0.59 cm, 5th ring 0.336 cm. $R=100$ cm. Calculate $\lambda$.	2018, 2024
Diffraction Grating	Deduce the missing order for a double slit Fraunhoffer diffraction pattern if the width of the slit and the opaque space are 0.16 and 0.8 mm respectively.	2018
Diffraction Grating	A plane grating has 15000 lines per inch. Find the angle of separation of the 5048 $\text{A˚}$ and 5016 $\text{A˚}$ lines of helium in the second order spectrum.	2016
Diffraction Grating	Plane transmission grating. Angle of diffraction for 2nd order principal maximum for $\lambda =5\times 10^{-5}$ cm is $30^{\circ }$. Calculate the number of lens (lines) in one cm of the grating surface.	2023
Polarization (Brewster)	Calculate the Brewster’s angle of light which travels from air into the glass medium ($\mu =1.55$) into the air medium.	2021
Polarization (Brewster)	Refractive index of crown glass 1.52. Find polarizing angle. If polarizing angle is about $59.50^{\circ }$, find refractive index of glass.	2023
Specific Rotation	Calculate the specific rotation of a given sample of sugar solution if the plane of polarization is turned through 26.4°. The length of the tube containing 20% sugar solution is 20 cm.	2017, 2019
Geometrical Optics	Two thin convex lenses $f_1=20$ cm, $f_2=2$ cm, separated by 2 cm. Calculate equivalent focal length and position of principal points.	2021

III. MODERN PHYSICS

Subtopic	Question (Numerical Input/Calculation Required)	Year(s)
Relativistic Mass	A man has a mass of 100 Kg on the ground. When he is in a rocket ship in flight, his mass is 101 Kg… What is the speed of the rocket ship?.	2017
Relativistic Mass	Man 70 Kg (ground). 71 Kg (in rocket). What is speed of rocket ship?.	2020
Length Contraction	A rocket ship is 100 m long on the ground. When it is in flight, its length is 99 m… What is its speed?.	2018, 2019
Photoelectric Effect	The photoelectric threshold frequency of silver is $0.86\times 10^{15}$ Hz. Calculate (i) the maximum kinetic energy, (ii) the stopping potential for $4\times 10^{15}$ Hz UV light.	2019
Photoelectric Effect	Metal threshold wavelength $6000\text{A˚}$. Calculate stopping potential when irradiated with (i) monochromatic light $\lambda =4000\text{A˚}$, (ii) light having twice the intensity and frequency.	2024
Compton Scattering	X-ray photon of wavelength 0.3 $\text{A˚}$ undergoes a 60° Compton scattering. Find the wavelength of scattered photon and kinetic energy imparted to the recoiling electron.	2016
Compton Scattering	X-ray scattered by free electron. At 45°, ${\lambda }^{\prime }=0.22\text{A˚}$. What is the wavelength of direct beam?.	2017
De-Broglie Waves	An electron has de-Broglie wavelength of 2 PM. Find its Kinetic energy and the phase & group velocities of its de-Broglie waves.	2021
De-Broglie Waves	Calculate the wavelength associated with a thermal neutron of energy 0.025 eV.	2022
Bohr Model (Wavelength)	Find the wavelength of the spectral line corresponding to the transition in the hydrogen atom from $n=4$ to $n=2$ state.	2020
Bohr Model (Energy)	How much energy is required to remove an electron in the $n=2$ state from a Hydrogen atom?.	2018
Radioactive Decay	Half-life of ${\text{U}}^{238}$ is $4.51\times 10^9$ years. What percentage of ${\text{U}}^{238}$ that existed $10^{10}$ years ago still survives?.	2019, 2021, 2022
Radioactive Decay	Half life of Radium is 1600 years. In how many years will $1$ gm of pure radium lose (i) one centigram, and (ii) be reduced to $1$ centigram.	2020, 2024
Radioactive Activity	Half-life of Radium is 26.8 minutes. Calculate the amount of ${\text{Ra}}^{214}$ which activity is 1 curie.	2017
Radioactive Decay	Half-life of Radon is 3.82 day. Find the time of decay to 60% of it.	2018
Nuclear Energy	Calculate the mass defect and binding energy of a deuteron.	2016
Nuclear Energy	Calculate the binding energy of a neutron in the ${}_3^7\text{Li}$ nucleus. Express the result in joules.	2023
Nuclear Fission	Calculate the energy released in a fission of ${}^{235}\text{U}$ nucleus.	2016
Nuclear Power	Calculate rate of consumption of ${\text{U}}^{235}$ per year for Roppur Nuclear Power Plant operating at 250 megawatts.	2024
Uncertainty Principle	Lifetime of an excited state $10^{-8}$ s. Calculate the minimum uncertainty in the energy of the excited state.	2023