## Falling Cat

You have a symbolic falling cat. This cat is made up of two cylinders, a heavy one (the body) and a smaller one (the tail) as in the figure. You know the mass and dimensions of the falling cat and its tail. The tail rotates around the cat body to allow the cat to fall

## Electron position in H atom

For the ground state of Hydrogen please find the most probable value of  the electron position $r$. The probability that the electron is found between $r$ and $r+dr$ is $P=|R_{nl} (r) |^2*r^2 dr$ Here above $R_{nl} (r)$ is the radial function for hydrogen in the n, l state and $r^2*dr$ comes from the volume element

## Empty Sphere field and potential

An empty sphere is charged. (the inner and outer radii of the sphere are $R_0$ and $R$). Please find the empty sphere field and potential as functions of $R$. What is the difference between the cases when the sphere is free in space and when the sphere is grounded? When the sphere is not grounded,

## 1D two particles system (Lagrangian)

You are given a 1D two particles system that have an attractive force between them $F=-kr^2$. Use the general coordinates $X$ (position of CM) and $d$ (distance between masses). A) Please write the Lagrangian of this system. B) Please specify the symmetry of this Lagrangian. C) Please specify what is the conserved quantity of this

## Car Tire Presssure. Zenner Regulator

Prior to a street venture you verify the tire pressure on every one of the 4 tires  worn out on your auto. You discover each is at 32 psig. The surrounding temperature is 60F. You start riding and get to be in the a forsaken road inside the focal point of the day. Because of

## Coaxial Cylindrical Capacitor

A cylindrical capacitor is made up from two concentric cylinders ($R$ and $2R$). Inside the 2R cylinder there is a dielectric from 2R to 1.5R of constant $k=3$. The charges are Q on the R cylinder and -Q on the 2R cylinder. a) Please find the electric field between r=0 and r=3R. b) Please find

## Swinging Pendulum (Quantum)

You are given a pendulum that swings having length $l=10 cm$. The amplitude of swinging is $A=1 cm$ ($\theta=0.1 rad$) for a mass $m=1 gm$  a)      Please find the total energy in ergs of this pendulum.b)      Please find the minimum energy quanta of this pendulum (in ergs).c)       For one quanta absorbed or released please find