# Classical Mechanics [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 18 - 22 of 84

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## Question 18

Appeared in Year: *2015*

### Question

MCQ▾A particle with rest mass M is at rest and decays into two particles of equal rest masses , which move along the Z – axis. Their velocities are given by,

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## Question 19

Appeared in Year: *2012*

### Question

MCQ▾A particle of mass is attached to a fixed point by a weightless inextensible string of length . It is rotating under the gravity as shown in the figure.

The Lagrangian of the particle is,

Where, and are the polar angles.

The Hamiltonian of the particle is,

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## Question 20

Appeared in Year: *2012*

### Question

MCQ▾In a central force field, the trajectory of particle of mass , and angular momentum in plan polar coordinates in given by,

Where, is the eccentricity of the particle՚s motion. Which one of the following choices for gives rise a parabolic trajectory?

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## Question 21

Appeared in Year: *2016*

### Question

MCQ▾The Lagrangian of a system is given by

, where are constants.

Which of the following is conserved?

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## Question 22

Appeared in Year: *2012*

### Question

MCQ▾Two uniform thin rods of equal length and masses and are joined together along the length. The moment of inertia of the combined rod of length about an axis passing through the mid – point and perpendicular to the length of the rod is –

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