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[Solved/QM-20003] Quantum Mechanics --- Solved Problem

Node id: 2261page
kapoor's picture 22-02-27 17:02:46 n

[Solved/QM-20002 ] Quantum Mechanics --- Solved Problem

Node id: 2260page
kapoor's picture 22-02-27 17:02:12 n

[SolvedQM-20001] Quantum Mechanics --- Solved Problem

Node id: 2259page
kapoor's picture 22-02-27 17:02:04 n

[Solved/QM-19001] Quantum Mechanics Solved Problem

Node id: 2256page
kapoor's picture 22-02-27 16:02:02 n

[Solved/QM-17003] Quantum Mechanics ---- Solved Problem

Node id: 2255page
kapoor's picture 22-02-27 16:02:19 n

[Solved/QM-17002] Quantum Mechanics Solved Problem

Node id: 2254page
kapoor's picture 22-02-27 16:02:10 n

[Solved/QM-17001] Quantum Mechanics --- Solved Problem

Node id: 2253page
kapoor's picture 22-02-27 16:02:40 n

[Solved/EM-04004] A point charge and an insulated conducting sphere at potential \(\phi_0\)

Node id: 2231page
kapoor's picture 22-02-27 16:02:00 n

[Solved/EM-04003] Charged sphere and a point charge

Node id: 2230page

An insulated conducting  sphere carries total charge \(Q\) and a charge \(q\) is placed at a distance \(a\) from the centre of the sphere. Find the potential at an arbitrary point outside the sphere.

kapoor's picture 22-02-27 16:02:32 n

[Solved/EM-02001] Two unifromaly charged overlapping spheres

Node id: 2222page
kapoor's picture 22-02-27 16:02:58 n

[QUE/CM-01018#Solu] Sliding rope (Solved)

Node id: 2430page

Falling rope: A rope of length $L$ slides over the edge of a table. Initially a piece $x_0$ of it hangs without motion over the side of the table.Let $x$ be the length of the rope hanging vertically at time $t$. The rope is assumed to be perfectly flexible. Show that the principle of  energy in the form of $T+V$ gives an integral of motion.

Source::SOMMERFELD


 

kapoor's picture 22-02-27 16:02:17 n

[QUE/CM-01012#Solu] -- Motion on Curves (Solved)

Node id: 2424page

A particle of mass $m$ moves on a cycloid under influence of uniform gravitational field. The parametric equations of the cycloid are given by $$ x= R( \phi + \sin\phi) , \qquad y=R(1-\cos\phi).$$ Find a suitable transformation to show that the equations of motion is identical to that of a simple harmonic motion  with frequency $\omega=g/4R$.

Source{Sommerfeld}


 

kapoor's picture 22-02-27 16:02:16 n

[QUE/CM-01009] Periodic Motion $V(x) = V_0 \left( \exp(-2x/\alpha) - 2 \exp(-x/\alpha)\right) $ (Solved)

Node id: 2416page

Find the equilibrium position and the frequency of small oscillations about the equilibrium position for the potential $c$

[HSM 42(a)]


 

kapoor's picture 22-02-27 16:02:51 n

[QUE/CM-01003#Solu] Periodic Motion $\displaystyle V(x) = V_0 \tan^2(\alpha x) $

Node id: 1910page

Question : For a particle in one dimensional potential well  $\displaystyle V(x) = V_0 \tan^2(\alpha x) $ find the time period as function of the energy of the particle.
Answer : $\displaystyle ({\pi\over\alpha})\sqrt{2m\over (E+V_0)} $

kapoor's picture 22-02-27 16:02:27 n

[QUE/CM-01017#Solu] Falling Chain (solved)

Node id: 2429page

 A chain lies pushed together at the edge of a table, except for a piece which hangs over it, initially at rest. The links of the chain start moving one at a time; neglect friction. The energy written in the usual form is no longer an integarl of motion. Instead impulsive  ( Carnot)  energy loss must be taken into accountb in writing the balance of energy.

Source::Sommerfeld


 

kapoor's picture 22-02-27 16:02:37 n

[Solved/QM-13001#Example]

Node id: 1384page
kapoor's picture 22-02-27 16:02:42 n

[QUE/CM-02001#Solu] Classical Mechanics Solved Problem

Node id: 1390page
kapoor's picture 22-02-27 16:02:14 y

[QUE/GT-02003#Solu] Group Theory Solution to Problem

Node id: 1429page
kapoor's picture 22-02-27 16:02:33 n

[QUE/GT-06001#Solu] Solved Problem

Node id: 1435page

GT-06 Solved Problem

Irreducible representations in direct product of two irreducible representations of $S_3$

kapoor's picture 22-02-27 16:02:54 n

[Solved/EM-03001] Electric Potential due to Uniform Charge on Surface of a Cone

Node id: 2223page

A conical surface ( an empty ice cream cone ) carries a uniform a uniform  surface charge density $\sigma_0$. The height of the cone and the radius of the base are  both equal to $a$. Find the potentials at the vertex of the cone and at the center of the base.

<Griffiths>

kapoor's picture 22-02-27 15:02:09 n

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