# GATE (Graduate Aptitude Test in Engineering) Physics: Questions 638 - 643 of 659

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## Question 638

Residue Theorem and Applications

Appeared in Year: 2017

### Describe in Detail

Essay▾

The contour integral evaluated along a contour going from to along the real axis and closed in the lower half – plate by a half circle is equal to ________. (up to two decimal places.)

### Explanation

Here, given contour integral is,

Poles of given function are,

Since, we have to evaluate integral along a contour going from to along the real axis and closed in the lower half – plate by a half circle. Therefore, only pole is considered.

Where,

The residue of at is,

… (1 more words) …

## Question 639

Appeared in Year: 2017

### Question

MCQ▾

Consider a one – dimensional potential well of width . Using the uncertainty principle , an estimate of the minimum depth of the well such that it has at least one bound state for an electron is :

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question 640

Appeared in Year: 2017

### Describe in Detail

Essay▾

A free electron of energy is incident upon a one – dimensional finite potential step of height . The probability of its reflection from the barrier is ________ (up to two decimal places) .

### Explanation

Here, .

The probability of reflection from barrier is given as,

## Question 641

Appeared in Year: 2017

### Question

MCQ▾

The Poisson bracket is equal to:

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question 642

Appeared in Year: 2017

### Describe in Detail

Essay▾

The decays at rest to and . Assuming the neutrino to be massless, the momentum of the neutrino is . (up to two decimal places)

### Explanation

The process of decay of is given as,

Here, a pion at rest decays into and . Therefore momentum of the pion is zero.

Now, according to conservation of energy,

And according to conservation of momentum,

Negative sine indicate, momentum of muon and that of neutrino are in opposite direction to each other.

Now, energies of particles: pion, muon and neutri…

… (8 more words) …

## Question 643

Appeared in Year: 2017

### Describe in Detail

Essay▾

Tree charges are placed at the vertices of an equilateral triangle of side as shown in the figure. The component of the electric dipole moment about the marked origin along the direction is .

### Explanation

Here, the electric dipole moment is expressed by,

Where, is the displacement vector pointing from negative charge to the positive charge. The electric dipole moment vector is also having same direction as displacement vector .

From given situation, the charges of the dipole are and , separated by the distance (altitude of triangle ) . Therefore, r…

… (3 more words) …

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