AP EAMCET · PHYSICS · Motion In Two Dimensions

A uniform rod of length $l$ and density $ρ$ is revolving about a vertical axis passing through its one end. If $ω$ is the angular velocity of the rod then the centrifugal force per unit area of the rod is

A $\frac{ρ ω^{2} l^{2}}{4}$
B $\frac{ρ ω^{2} l^{2}}{12}$
C $\frac{ρ ω^{2} l^{2}}{2}$
D $\frac{ρ ω^{2} l^{2}}{8}$

Verified Solution

Answer & Solution

Correct Answer

(C) $\frac{ρ ω^{2} l^{2}}{2}$

Step-by-step Solution

Detailed explanation

Take an element of length dx and mass dm at a distance x from the rotating end. Here mass of elemental part dm=ρdx Centrifugal force on this small element dF=dm xω2 Total centrifugal force, F=∫dF=∫0lρxω2dx ⇒ F=ρω2l22

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A uniform rod of length l and density ρ is revolving about a vertical axis passing through its one end. If ω is the angular velocity of the rod then the centrifugal force per unit area of the rod is

Step-by-step Solution

A uniform rod of length $l$ and density $ρ$ is revolving about a vertical axis passing through its one end. If $ω$ is the angular velocity of the rod then the centrifugal force per unit area of the rod is