A block $(P)$ is rotating in contact with the vertical wall of a rotor as shown in figures $\mathrm{A},…

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. $\left(R_A \lt R_B \lt R_C \text { radii }\right)$
  1. $\omega_A \lt \omega_B \lt \omega_C$
  2. $\omega_A=\omega_B=\omega_C$
  3. $\omega_C \lt \omega_B \lt \omega_A$
  4. $\omega_C=\omega_A+\omega_B$

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, $R_A \lt R_B \lt R_C \Rightarrow \frac{1}{\omega_A^2} \lt \frac{1}{\omega_B^2} \lt \frac{1}{\omega_C^2}$ $\therefore \quad \mathrm{W}_{\mathrm{A}}\gt\mathrm{W}_{\mathrm{B}}\gt\mathrm{W}_{\mathrm{C}}$

Asked in: AP EAMCET 2024 (20 May Shift 2)

Practice more Motion In Two Dimensions questions on Aicharya