Questions tagged [homework-and-exercises]

Applies to questions of primarily educational value - not only questions that arise from actual homework assignments, but any question where it is preferable to guide the asker to the answer rather than giving it away outright. Please READ THE GUIDANCE IN META before asking homework-like questions.

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Electrostatics Question For JEE [closed]

A Conducting Sphere Has Charge Q uniformly distributed over its surface.Let a Gaussian Surface of same radius but passing through the centre of the same sphere. The total flux linked with the Gaussian ...
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1 answer
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Its a physics exam question, I and my friend don't understand the theory and mechanics behind it [closed]

Two spheres each of mass m are connected by string of length 2l, are kept on a smooth horizontal surface. A vertical force F is applied at the middle of the string. What is the max value of F for ...
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A question regarding electric field and charges inside a conductor

In this figure there is a positive point charge in the cavity and it creates an electric field, this polarises the charges in the conductor and the negative charges move towards the cavity where the ...
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Find interval between scucessive conjunctions

The maths here doesn't seem to be too hard, but for some reason I can't quite figure out what to do: Consider two planets orbiting a star in circular orbits with periods $T_1$ and $T_2$. What is the ...
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0 votes
1 answer
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Ladder Operators Calculate Inner Product

We have the step-down and step-up ladder operators, and I am trying to calculate $\langle\alpha|a^†aa^†|\alpha\rangle$, I know that $a|\alpha\rangle = \alpha|\alpha\rangle$ and $|\alpha\rangle$ is ...
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Exercise 32 from Bernard Schutz

The exercise In Bernard Schutz's 'General Relativity, there is an exercise, I don't understand how to start with. To develop a TT Gauge, we should use the given transformation. But somehow I am ...
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Finding a new hamiltonian from a given canonical transformation

Let us suppose we have a given Hamiltonian $$H = \frac{P_1^2}{4}+\frac{P_2^2}{2}+V(Q_2)$$ and $q_1 = Q_1 + Q_2/2$ with $q_2 = Q_1 - Q_2/2$. I need to find the new hamiltonian by using these canonical ...
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Flux linked with coil [closed]

when a super conducting loop with zero resistance is moving towards a magnetic, the flux linked with the loop is a) Increases b) Decreases c) Remains constant d) First increases then decreases
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1 answer
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Symmetrical, spherical charge distribution [closed]

I have this problem from my Electromagnetism class, but I don´t have a lot of idea in how to solve it. Show that for a symmetrical, spherical charge distribution $\rho(\vec{r})=\rho(r)$ (with $r$ ...
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2 answers
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Net bound surface charge density of capacitor

Q. In a parallel plate capacitor, two dielectric slabs of thickness 5 cm each are inserted between the plates and a potential of 100 V is applied across it. The value of the net bound surface charge ...
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How to (derivate and) apply the electric field formula? [closed]

this question might be straightforward but I'm getting lost and I feel like I wouldn't be able to proceed if I don't get this clear from the get-go. I get the basic idea behind finding the electric ...
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0 answers
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Finding equation for acceleration of a mass connected to a massless spring [closed]

If a mass of $ 5$ kg connected to one end of a spring is released from the elongated position and its corresponding angular velocity is governed by the equation $ \omega =t^3+t^2+1 $ then what is its ...
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2 answers
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Hooke's law and modulus of elasticity [closed]

I'm having trouble in understanding the following question which state modulus of elasticity in Newton. Is it possible that we can define modulus of elasticity in Newton somehow?? I am getting a wrong ...
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0 votes
1 answer
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Konig's Theorems

In the proof of Konig's Theorems the following identity is used: $$ \underline{v_i} = \underline{v_i'} + \underline{v_c} $$ which is the law of transformation of velocity when passing from the ...
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Question about quantum scattering theory (elastic) [closed]

I tried to solve this question and reach to this: J1=ħ/m Im[ψ*(incident)dψ/dz]=ħk/m J2=ħ/m Im[ψ*(scattered)(gradient ψ)] =ħ/m Im[f*(θ) (e^-ikr)/r (d/dr +1/r d/dθ+1/rsinθ d/dφ) (f(θ) e^ikr)] =ħ/m Im[|...
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1 vote
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On reciprocal lattice properties

As a consequence of the translational invariance of an ideal crystal, it's reasonable to assume that this periodicity must be recognised in any function $f({\mathbf r})$ of physical interest for the ...
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1 vote
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Proving a relationship involving the chemical potential [closed]

I need to prove the relation $$\left(\frac{\partial \mu}{\partial N}\right)_{T,V}> \left(\frac{\partial \mu}{\partial N}\right)_{T,P}.$$ One may start with the total differential of the internal ...
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0 votes
2 answers
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Maintaining the balance of a rod of uniform density

Assume a rod which: is of uniform density $\rho$. is a metre long. The rod is balanced on a knife edge at 58 cm. mark (in the notation where the extreme left side is assumed to be 0). To the extreme ...
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Extension in Massive Springs under gravity

Suppose we have a spring which has a uniform cross sectional area $A$, and has a uniform linear mass density $J$, and has a total unstretched length $L$. Let the spring also obey Hooke's Law. Further, ...
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1 answer
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Obtaining the KG equation from Action

After solving the field equation for $$S = \int \sqrt{-g}dx^4[f(\phi)R + h(\phi)g^{\mu \nu}\nabla_{\mu}\phi\nabla_{\nu}\phi - V(\phi)]$$ I have obtained $$2h\square \phi + \frac{\partial h}{\partial \...
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Moment of inertia of a cylinder with variable density [closed]

I have a cylinder with radius $R$ and a density that depends on the radius as follows: $ρ = ar$, where $a$ is just some constant. I tried to find its moment of inertia this way: $$ I=\int_0^R{r^2dm} \\...
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-1 votes
0 answers
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Intensity pattern in Double slit experiment [closed]

This question appeared in my yearly exams regarding the intensity distribution of bright fringes in YDSE . If the screen is brought closer to the plane of slits , does the intensity of bright fringes ...
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-1 votes
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Electric field strength [closed]

I have got a problem to solve which is quite a way out of my understanding and was looking for help: A thin, horizontal, straight rod evenly charged throughout the whole length, which is 2a, is in a ...
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-1 votes
1 answer
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Probabilities of eigenfunctions

I am struggling to understand how to get the probabilities of each eigenstate occurring from a wavefunction that is a linear combination of eigenfunctions. If we have a wavefunction $$\Psi = A ( e^{...
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0 votes
3 answers
37 views

Is electric potential inversely proportional to the voltage at a point?

Consider this simple diagram, where the thermistor's resistance = $500\Omega$. Let's suppose the temperature of the room increases. Then, Electric potential at point ...
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1 answer
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Question regarding exercise of dynamics of spin-1/2 system

Problem 5) Generic Quantum-Mechanical Spin-1/2 Dynamics Consider a spin-1/2 system in an external magnetic field, described by $H=\mu_s\mathbf{B}(t)\cdot\hat{\mathbf{S}}$ with $$\mathbf{B}(t) = B_0\...
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0 votes
2 answers
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Variation for the Canonical Scalar Field in $f(\phi)R$

I am trying to find the Field equation for $$S = \int \sqrt{-g}dx^4[f(\phi)R + h(\phi)g^{\mu \nu}\nabla_{\mu}\phi\nabla_{\nu}\phi - V(\phi)$$ but I could not take the variation of $$\delta(\sqrt{-g}h(\...
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Energy Density of Charged Non-Conducting Sphere

I know how the Energy density of conducting and non-conducting shells is derived by using the argument of electrostatic pressure. It comes out to be ½(E²ɛ₀).But when I try to derive it via the same ...
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Tensor Product in Index Notations

I have been reading a book on continuum mechanics and I encountered the equations shown below. I have no idea how the author managed to go from equation 3.16 to equation 3.18. Could someone help me ...
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1 answer
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Projectile launch question [closed]

The question refers to the following information: What would the Olympic Games on the Moon be like? This article was recently published in the magazine Mundo Estranho, Editora Abril, written by Tiago ...
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0 answers
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Mechanics | Use the work-energy principle to find the speed of the book as it hits the floor [closed]

Problem A small book of mass $m$ is held on a rough straight desk lid which is inclined at an angle $\alpha$ to the horizontal, where $\tan\alpha=\frac34$. The book is released from rest at a distance ...
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0 votes
0 answers
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Transition probability for a time dependent perturbed quantum oscillator [closed]

I'm trying to solve a time-dependant perturbation theory type of problem which I've never seen before. Time-dependant perturbation theory applies for a Hamiltonian in the form: $\hat H = \hat H_0 + V(...
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0 votes
3 answers
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Is there a contradiction at the top of this circuit?

Applying kirchhoff's second law to the first loop, the current in the upper branch remains determined and is $2.4$ A to the right (if $i$ is to the right then $-10i + 24 = 0$). Then the current in the ...
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2 votes
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Equation of motion in quadratic gravity

I am going through the paper https://arxiv.org/abs/1502.01028 which considers the quadratic gravity with the action \begin{align} S = \int d^4x \sqrt{-g} (R - \alpha C_{\mu\nu\rho\sigma}C^{\mu\nu\rho\...
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0 votes
0 answers
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Vectors in different coordinate systems [closed]

The answer for the first question is "The wind blows from $40.5^\circ$ NE". But I think it is impossible. The following is how I do the first question. Set that $\mathbf{i}$ is the unit ...
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2 votes
2 answers
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A simple proof that under Newtonian gravity rotating massive bodies are ellipsoids?

Here is my attempt at deriving the shape of an idealized rotating massive body under Newtonian gravity, assuming that the gravity force points towards the center of mass and shape of the body is ...
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1 answer
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How does the direction of a force applied to a pulley influence the pulley's motion?

Suppose friction is negligible, we want to determine the force F that has to be applied to a pulley (whose radius is $R$) such that the body m has a constant acceleration a, which is given. What I did ...
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-1 votes
1 answer
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The image contains the question. The image descriptions contains my DOUBT

When the charges are at the extreme positions, the velocities of both the charges will be zero. DOUBT : Can we say that the net force acting on both the charges at the extreme position is also equal ...
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Question about wave packet shape [closed]

(a) A free proton is localized within ∆x = 10−10m. Estimate the time ts it takes the packet to spread appreciably. Repeat for an proton localized within 1 cm. (b) Consider a wave packet that satisfies ...
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Electrolysis of a solution of $\rm Ni(NO_3)_2$

This is a problem given in my textbook A current of $3.7 amp$ is passed for 6 hours between inert electrodes in 0.5 litres of 2M solution of $\rm Ni(NO_3)_2$. What will be molarity of the solution ...
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The ideal gas equation is $pV=nRT$. Prove that $p=\frac{\rho RT}{M}$

The ideal gas equation is $$pV=nRT$$ Show that the pressure exerted by a fixed mass of gas is given by the equation $$p=\frac{\rho RT}{M}$$ Where $\rho$ is the density of the gas and $M$ is the mass ...
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-3 votes
0 answers
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Boat River Problem (Relative motion) [closed]

On a river coast, there is a port; when a barge passed the port, a motor boat departed from the port to a village at the distance s1 = 15 km downstream. It reached its destination After 45 min, turned ...
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-1 votes
0 answers
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Calculate the transition amplitude and the differential cross section [closed]

Calculate the transition amplitude and the differential cross section for the lowest order process in perturbation theory in which a photon strikes an electric charge core Ze and the heavy core ...
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0 votes
0 answers
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Collision of $\rm H$ atoms [closed]

The question is: Two $\rm H$ atoms in the ground state collide inelastically. The maximum amount by which their combined kinetic energy is reduced by__________ well in this question I solved it ...
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0 votes
0 answers
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Radiation Intensity from a point charge in a circular motion around a static charge [closed]

A particle with charge $-q$ moves with a uniform angular velocity $\omega$ in a circular orbit of radius $a$ in the $xy$-plane, around a fixed charge $+q$, which is at the centre of the orbit at $(0,0,...
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0 votes
0 answers
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Effective masses of spring-mass systems [duplicate]

It is known that the effective mass of the spring in this vertical spring-mass system(figure can be viewed by the following Wiki link) is 1/3 of the mass of the spring, for example, if the mass of ...
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0 votes
0 answers
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Lagrangian and Newtonian Equations of motion with Atwood Machine [closed]

I just have one quick question. As these are simply different methods, are all results compatible? For example, if I find the acceleration of each of the three masses in the double Atwood machine ...
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0 votes
1 answer
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Why do equation of motion fail to apply in non-inertial frame even after applying pseudo force?

I considered two cars of equal mass moving towards each other with speed 30m/s and 18 m/s respectively and when they are 100 meters apart they both start de accelerating at 6m/s² each. So if we ...
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0 votes
1 answer
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Ammeter readings of variable resistor

Question The diagram in question has no numerical values. $R_1$ is a resistor of constant resistance. $R_2$ is a variable resistor set to minimal resistance. $V$ is an ideal voltmeter. $A_1$ & $...
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0 votes
2 answers
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Time taken by the pendulum to complete one oscillation with initial angle $ \theta = 90° $

The question that I have is pretty much the question in the image below. The question was given to my class (11th grade) by our physics teacher as a challenge problem. I think this is important to ...
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