# Classical Mechanics [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 82 - 84 of 84

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## Question 82

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 83

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 84

### Question

MCQ▾The Lagrangian for a particle of mass at a possible moving with velocity is given by

, where is a potential and is a constant. If is the canonical momentum, then its Hamiltonian is given by,

### Choices

Choice (4) | Response | |
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a. | ||

b. | ||

c. | ||

d. |