# Optionals IAS Mains Physics: Questions 156 - 161 of 306

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## Question 156

Appeared in Year: *2016*

### Describe in Detail

Essay▾Find the centre of mass of a homogeneous semicircular plate of radius.

### Explanation

- Here too the centre of mass obviously lies on the line of symmetry (Fig (1) ) passing through the mid – point of the base and perpendicular to it. Since it is a homogeneous plate, the centre of the mass will be at a distance from , given by relation , where is the mass of an element of it of radius and , the mas of the whole plate.

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## Question 157

Appeared in Year: *2007*

### Describe in Detail

Essay▾Determine the discrete energy levels and the corresponding Eigen functions for a particle in an infinitely deep potential well inside a cube of dimension , i. e. assume for elsewhere

### Explanation

A particle in this potential is completely free, except at the two ends and , where an infinite force presents it from escaping.

Outside the well, (the probability of finding the particle there is zero). Inside the well, where, the time independent Schrodinger equation

Becomes

Or

Where

Here we

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## Question 158

### Explanation

Experimentally, there is no evidence for the existence of any excited states of the deuteron. Indeed, extending the calculations of the bound states to the cases where the orbital angular momentum quantum number is greater than zero leads to the result that the deuteron can’t exist in these states. It will be assumed that the potential is central

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## Question 159

Appeared in Year: *2016*

### Describe in Detail

Essay▾Write down the salient features of the Einstein’s theory of lattice heat capacity. Further write down the expression for specific heat in Einstein’s theory and explain it’s high and low temperature limits.

### Explanation

- The salient features of the Einstein’s theory are listed below:

- A crystal consists of atoms which may be regarded as identical and independent harmonic oscillators.
- A solid consisting of atoms is equivalent to one dimensional harmonic oscillators.
- All the oscillators vibrate with the same natural frequency due to the identical environment of each.
- Th

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## Question 160

Appeared in Year: *2016*

### Describe in Detail

Essay▾Explain in detail L–S coupling and j–j coupling schemes.

### Explanation

**L–S coupling:**

- The L–S coupling is also known as “Russell - Saunders” coupling. In atoms which obey this coupling we introduce the various perturbations in the order: (a) spin – spin correlation (b) residual electrostatic interaction (c) spin – orbit interaction

**(a) As a result of spin** – spin correlation effect, the individual spin angular momentum ve

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## Question 161

Appeared in Year: *2016*

### Describe in Detail

Essay▾Four solid sphere each of mass and radius , are placed with their centre on the four corners of a square of side as shown in figure below:

Calculate the moment of inertia of the system about one side of the square. Also calculate the moment of inertia of the system about a diagonal of the square.

### Explanation

Let be the four solid spheres, each of mass and radius placed at the four corners of the square as shown and let it be required to calculate the M. I. of the system about the side of the square.

Clearly, lies along the diameter of each of the spheres so that M. I. of each about

And t

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