A rigid body rotates about a fixed axis with variable angular velocity (α - β t) at time t, where α and β are constants. The angle through which it rotates before it comes to rest is (a) (α)/(β) (b) (α²)/(β) (c) (α²)/(2β) (d) (α)/(2β)

Answer: (c). ω = α - β t = 0 at t = (α)/(β). θ = ∫₀α/β (α - β t) dt = α t - (β t²)/(2) θ = (α²)/(β) - (α²)/(2β) = (α²)/(2β) So the answer is (c) (α²)/(2β).

A rigid body rotates about a fixed axis with variable angular… | MHT CET 2025 (26 Apr, Shift 1)

Q15MHT CET 2025 · 26 APR · SHIFT 1Medium

Rotational Kinematics & Dynamics

A rigid body rotates about a fixed axis with variable angular velocity $(\alpha - \beta t)$ at time $t$ , where $\alpha$ and $\beta$ are constants. The angle through which it rotates before it comes to rest is

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Answer: (c)

$\omega = \alpha - \beta t = 0$ at $t = \frac{\alpha}{\beta}$ .
$\theta = \int_0^{\alpha/\beta} (\alpha - \beta t)\,dt = \alpha t - \frac{\beta t^2}{2}$
$\theta = \frac{\alpha^2}{\beta} - \frac{\alpha^2}{2\beta} = \frac{\alpha^2}{2\beta}$
So the answer is (c) $\frac{\alpha^2}{2\beta}$ .

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