A body is rotating with kinetic energy E. If angular velocity of body is increased to three times of initial angular velocity then kinetic energy become nE. Find n.

Question

A cylindrical tube \(AB\) of length \(l\), closed at both ends, contains an ideal gas of \(1\) mol having molecular weight \(M\). The tube is rotated in a horizontal plane with constant angular velocity \(\omega\) about an axis perpendicular to \(AB\) and passing through the edge at end \(A\), as shown in the figure. If \(P_A\) and \(P_B\) are the pressures at \(A\) and \(B\) respectively, then (consider the temperature to be same at all points in the tube)

Answer 1

Given:
Initial kinetic energy = E
Final angular velocity = 3ω

Step 1: Formula of rotational kinetic energy
K = (1/2) I ω²

Step 2: Relation
K ∝ ω²

Step 3: New kinetic energy
K' ∝ (3ω)² = 9ω²

Step 4: Compare
K' = 9E

Final Answer: n = 9

A body is rotating with kinetic energy E. If angular velocity of body is increased to three times of initial angular velocity then kinetic energy become nE. Find n.

Solution and Explanation

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