Question

A particle bound to move on the inner surface of a parabolic revolution has degress of freedom

Answer 1

$\huge{\underline{\underline{\huge{\bold{AnsweR \: :-}}}}}$

Degree of freedom is defined as the minimum number of parameter using which you can define the system.

Now, for this case, consider the spherical coordinate system. For a particle confined to the surface of sphere, the distance from the origin remains constant but the other coordinates (theta and phi) can vary, hence degree of freedom 2.

To simplify it further, think of Earth as a sphere, and you are on its surface, you cannot fly or go into the ground. Then your movement is confined over the surface of Earth.

To you, the surface is just like a 2-dimensional surface on which you can move, hence you have degree of freedom 2.