Q130 / 160 · AP EAMCET 2024 (20 May Shift 2) · Physics
A block $(P)$ is rotating in contact with the vertical wall of a rotor as shown in figures $\mathrm{A}, \mathrm{B}, \mathrm{C}$. The relation between angular velocities $\omega_A, \omega_B$ and $\omega_C$ so that block does not slide down.
$\left(R_A \lt R_B \lt R_C \text { radii }\right)$
- A$\omega_A \lt \omega_B \lt \omega_C$
- B$\omega_A=\omega_B=\omega_C$
- Correct answerC$\omega_C \lt \omega_B \lt \omega_A$
- D$\omega_C=\omega_A+\omega_B$
Solution
For the block P,
$\begin{aligned}
& N=m \omega_A^2 R_A=m \omega_B^2 R_B=m \omega_C^2 R_C \\
& \Rightarrow R_A: R_B: R_C=\frac{1}{\omega_A^2}: \frac{1}{\omega_B^2}: \frac{1}{\omega_C^2}
\end{aligned}$
As, $R_A \lt R_B \lt R_C \Rightarrow \frac{1}{\omega_A^2} \lt \frac{1}{\omega_B^2} \lt \frac{1}{\omega_C^2}$ $\therefore \quad \mathrm{W}_{\mathrm{A}}\gt\mathrm{W}_{\mathrm{B}}\gt\mathrm{W}_{\mathrm{C}}$
As, $R_A \lt R_B \lt R_C \Rightarrow \frac{1}{\omega_A^2} \lt \frac{1}{\omega_B^2} \lt \frac{1}{\omega_C^2}$ $\therefore \quad \mathrm{W}_{\mathrm{A}}\gt\mathrm{W}_{\mathrm{B}}\gt\mathrm{W}_{\mathrm{C}}$
Hence, the correct answer is option: 'C'.