Question

What is the degree of freedom of a particle in a three-dimensional space that cannot move in y direction.

Answer 1

A particle in a 3 dimensional space (x, y, z axes) that cannot move in the y direction has 2 degrees of freedom. It can still move freely along the x and z axes.

Degrees of freedom refer to the number of independent displacements (or motions) that a particle can make. Since this particle cannot move along the y axis, it only has 2 independent motions it can make:

Displacement along the x axis

Displacement along the z axis

So it has 2 degrees of freedom, one for each independent motion (displacement along x and z).

In general, for an n-dimensional space where m dimensions have constrained or fixed movement, the degrees of freedom will be:

Degrees of freedom = n - m

In this case:

n = 3 (since it's a 3D space - x, y and z axes)

m = 1 (y dimension has constrained movement)

Therefore:

Degrees of freedom = 3 - 1 = 2

So the final answer is that the particle has 2 degrees of freedom.

Answer 2

In a three-dimensional space where a particle cannot move in the y direction, its degree of freedom is reduced to two. The particle can move freely in the x and z directions, but its motion is restricted along the y-axis. This constraint eliminates one degree of freedom, leaving the particle with two remaining degrees of freedom.