# Classical Mechanics [Optionals IAS Mains Physics]: Questions 1 - 5 of 31

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## Question 1

Classical Mechanics
Conservation of Linear and Angular Momentum

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 2

Classical Mechanics
Generalised Coordinates and Momenta

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…

… (94 more words) …

## Question 3

Classical Mechanics
Cyclic Coordinates

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)

## Question 4

Classical Mechanics
Generalised Coordinates and Momenta
Edit

Appeared in Year: 2012 (IFS)

### Describe in Detail

Essay▾

Starting with Newton՚s second law of motion, establish D՚ Alembert՚s principle and discuss its significance? (Paper-1) (Section – A)

### Explanation

• Let consider a system described by generalized coordinates . And this system undergoes a certain displacement in configuration space. If for this displacement it does not take any time and it is consistent with the constraints on the system. This kind of displacement is called virtual.
• In virtual displacement there is no actual motion of the system…

… (206 more words) …

## Question 5

Classical Mechanics
Rotating Frames
Edit

Appeared in Year: 2013 (IFS)

### Write in Short

Short Answer▾

A satellite revolves in a circular orbit around the Earth at a certain height above it. Calculate the time period of revolution of the satellite, if the radius of the Earth is significantly higher than the height at which the satellite revolves. (Section A)