# Optionals IAS Mains Physics: Questions 188 - 193 of 307

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## Question 188

Appeared in Year: *2017*

### Describe in Detail

Essay▾State and explain stoker՚s law. A drop of water of radius is falling through a medium whose density is and . Find the terminal velocity of the drop of water. (Paper-1)

### Explanation

It is a common experience that a body falling through a viscous medium always encounters an opposing viscous drag, resulting in absorption of energy by the medium in the form of heat. And, if the motion of the body be fast enough even eddies and waves may be set up in the medium, absorbing still more energy.

This opposing force or viscous drag incre…

… (482 more words) …

## Question 189

Appeared in Year: *2005*

### Describe in Detail

Essay▾What do you understand by paraxial rays? Show that the effect of translation of a paraxial ray while travelling along a homogenous medium is represented by a matrix if the ray is initially defined by a matrix.

### Explanation

A ray is said to be paraxial if the angle between the ray and the principle axis (or symmetry axis) is small. Only rays inclined at less than about t the principle axis are considered as paraxial rays and they lie close to the axis throughout the distance from object to image. As the angles are small and when expressed in radians, we can set the …

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## Question 190

Appeared in Year: *2005*

### Describe in Detail

Essay▾The ground state wavefunction of a linear simple harmonic oscillator is calculate the constant A and the average values of Given that

### Explanation

Since the wavefunction is normalized so

As the function is an even function so

Put

As wavelength is normalized

As the is an odd function and

Formula used:

## Question 191

Appeared in Year: *2017*

### Describe in Detail

Essay▾Using Schrodinger equation, obtain the eigen functions and eigen values of energy for a 1- dimensional harmonic oscillator. Sketch the profile of eigen functions for first three energy states.

### Explanation

Let us write the Schrodinger equation for the harmonic oscillator

Things look a little cleaner if we introduce the dimensionless variable

In terms of the Schrodinger equation reads

Where is the energy, in units of

Our problem is to solve equation (2) and in the process obtain the allowed values of

(and hence of E.)

To begin with, note that at very la…

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## Question 192

Appeared in Year: *2018*

### Describe in Detail

Essay▾The wave function of a practical is given by . Find the probability of locating the particle in the range . **(Paper-II)**

### Explanation

Since the given wave function is normalized, the probability of finding the particle in the interval is given by

= [as the wave function is normalized ]

## Question 193

Appeared in Year: *2005*

### Describe in Detail

Essay▾Consider two long and straight current carrying wires placed parallel to other a certain distance apart. Derive an expression for the force per unit length experienced by these wires. Discuss that the attractive (repulsive) nature of this force is related to the directions of flow of currents in the two wires.

### Explanation

Let be two parallel wires separated by a distance and carrying currents and respectively.

The magnetic field induction produced at element , due to element , is

The magnetic induction is perpendicular to the plane containing and , and points into the paper.

The force exerted by the current car…

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