# Optionals IAS Mains Physics: Questions 1 - 5 of 307

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## Question 1

Appeared in Year: *2011 (IFS)*

### Write in Short

Short Answer▾Write down the expression for the Bose – Einstein distribution function and explain the meaning of the symbols used. (Paper-I) (Section - B)

## Question 2

Appeared in Year: *2011 (IFS)*

### Write in Short

Short Answer▾A particle of rest mass ‘M’ moving at a velocity ‘u’ collides with a stationary particle of rest mass ‘m’ . If the particle stick together, show that the speed of the composite ball is equal to,

Where (Paper-1) (Section – A)

## Question 3

Appeared in Year: *2011 (IFS)*

### Describe in Detail

Essay▾Obtain the term symbols for two singlet states and two triplet states for two electron atoms. (Paper-2) (Section-A)

### Explanation

If we knowing the value of various types of angular momenta, term symbols gives three kinds of information,

Total orbital angular momentum, L

Multiplicity of the terms,

Total angular momentum,

- We can do vector sums of these vector. But it becomes easy if we consider components as these add together as scalars.
- Theref…

… (130 more words) …

## Question 4

Appeared in Year: *2012 (IFS)*

### Describe in Detail

Essay▾Using D՚ Alembert՚s principle, show that the following relation can be obtained for a system of particles under generalized coordinates,

What is the significance of ? (Paper-1) (section – A)

### Explanation

- The mathematical statement of D՚ Alembert՚s principle is given as,

- Transform D՚ Alembert՚s principle into expressions containing independent generalized coordinates only.

- Equation (2) , gives an infinitesimal virtual displacement at particular instant . We can see that the variation with respect to time is absent in equation (2) because virtual disp…

… (93 more words) …

## Question 5

Appeared in Year: *2012 (IFS)*

### Write in Short

Short Answer▾Express Lagrange՚s equation of motion for the cyclic coordinate and show that the result leads to the general conservation theorem for the generalized momentum coordinates. (Paper - 1) (Section – A)