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BITSAT 2024
Exam
BITSAT
Year
2024
Subject
Physics
Chapter
Motion in Two Dimensions

BITSAT 2024 · Physics · Motion in Two Dimensions

A rigid body rotates about a fixed axis with variable angular...

A rigid body rotates about a fixed axis with variable angular velocity equal to α−βt\alpha-\beta t, at the time tt, where α,β\alpha, \beta are constants. The angle through which it rotates before it stops is

Options

  1. Aα22β\frac{\alpha^2}{2 \beta}
  2. Bα2−β22α\frac{\alpha^2-\beta^2}{2 \alpha}
  3. Cα2−β22β\frac{\alpha^2-\beta^2}{2 \beta}
  4. D(α−β)α2\frac{(\alpha-\beta) \alpha}{2}

Correct answer

A. α22β\frac{\alpha^2}{2 \beta}

Step-by-step solution

ω=α−βt\omega=\alpha-\beta t. Comparing with ω=ω0−αt\omega=\omega_0-\alpha t Initial angular velocity =α=\alpha Angular'retardation =β∴=\beta\therefore Angle rotated before it stops is α22β\frac{\alpha^2}{2 \beta}. [using ω2=ω02+2βθ]\left.\omega^2=\omega_0^2+2 \beta \theta\right]
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