# GATE (Graduate Aptitude Test in Engineering) Physics: Questions 653 - 658 of 659

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## Question 653

Appeared in Year: 2017

### Describe in Detail

Essay▾

A person weights at Earth՚s north pole and at the equator. Treating the Earth as a perfect sphere of radius , the value is ________. (up to two decimal places) . (Take )

### Explanation

The gravitational acceleration at pole of the earth is,

Therefore weight of a person at north pole of earth is,

And the gravitational acceleration at equator is,

Weight of a person at equator of earth is,

Now,

## Question 654

Appeared in Year: 2017

### Describe in Detail

Essay▾

The Compton wavelength of a proton is . (up to two decimal places) .

### Explanation

The Compton wavelength of proton is given as,

## Question 655

Appeared in Year: 2017

### Question

MCQ▾

The minimum number of NAND gates required to construct an OR gate is:

### Choices

Choice (4)Response

a.

2

b.

5

c.

4

d.

3

## Question 656

Appeared in Year: 2017

### Describe in Detail

Essay▾

Two identical masses of each are connected by a massless spring of spring constant . The non – zero angular eigen frequency of the system is . (up to two decimal places) .

### Explanation

From question, two identical masses of each are connected by a massless spring of spring constant .

Here, both masses are free to oscillate due to spring, therefore effective mass of system consider.

Now, the spring is supposed to obey Hooke՚s law, therefore when spring is extended or compressed by a distance from its natural length, the tension (o…

… (20 more words) …

## Question 657

Appeared in Year: 2017

### Describe in Detail

Essay▾

The energy density and pressure of a photon gas are given by and , where is the temperature and is the radiation constant. The entropy per unit volume is given by . The value of is ________. (up to two decimal places) .

### Explanation

The energy density of a photon gas is given as,

Since, ;

Now, Heat capacity is given by,

Now, entropy of photon gas is,

Entropy per unit volume,

According to question,

Substituting value of , from equation (1) ,

## Question 658

Appeared in Year: 2017

### Describe in Detail

Essay▾

A uniform volume charge density is placed inside a conductor (with resistivity ) . The charge density becomes of its original value after time seconds. (up to two decimal places)

### Explanation

According to charge conservation law, the time rate of decrease of charge within a given volume equal to the net outward current flow through the closed surface of the volume.

Let, the current coming out of the closed surface is

Where, is the total charge enclosed by closed surface.

Applying divergence theorem,

But,

Therefore equation (1) become,

This …

… (57 more words) …

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