Question:
A particle is constrained to move on a parabola \(y = kx^{2}\). The number of degrees of freedom is:
A particle is constrained to move on a parabola \(y = kx^{2}\). The number of degrees of freedom is:
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Two planar coordinates minus one holonomic constraint \(y=kx^{2}\) leaves one free coordinate.
Updated On: Jul 2, 2026
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The Correct Option is A
Solution and Explanation
Step 1: A free particle in a plane has 2 position coordinates, \(x\) and \(y\).
Step 2: The constraint \(y = kx^{2}\) is a single holonomic equation relating them.
Step 3: Degrees of freedom \(=\) number of coordinates \(-\) number of independent constraints:
\[f = 2 - 1 = 1.\]
Step 4: Physically, once \(x\) is chosen, \(y\) is fixed by the curve, so a single generalized coordinate (e.g. \(x\)) describes the motion.
\[\boxed{f = 1}\]
Step 2: The constraint \(y = kx^{2}\) is a single holonomic equation relating them.
Step 3: Degrees of freedom \(=\) number of coordinates \(-\) number of independent constraints:
\[f = 2 - 1 = 1.\]
Step 4: Physically, once \(x\) is chosen, \(y\) is fixed by the curve, so a single generalized coordinate (e.g. \(x\)) describes the motion.
\[\boxed{f = 1}\]
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