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

Correct Answer is : α22β{α²}{2 β}2βα2

Correct Answer is : α22β{α²}{2 β}2βα2

Test Index

MHTCET 26 Apr 2025 Shift 1 Paper

Question : 21 of 150

Marks: +1, -0

\alpha-\beta t

t

\alpha

\beta

Solution:

Concept:

The angle rotated is found by integrating angular velocity over time until the body stops.

Explanation:

The angular velocity is given as

\omega(t) = \alpha - \beta t

The body comes to rest when

\omega = 0

. So,

\alpha - \beta t = 0 \Rightarrow t = \frac{\alpha}{\beta}

The angle rotated is the integral of angular velocity from

t = 0

t = \frac{\alpha}{\beta}

\theta = \int_{0}^{\frac{\alpha}{\beta}} (\alpha - \beta t) \, dt

Evaluating the integral:

\theta = \left[\alpha t - \frac{\beta t^2}{2}\right]_{0}^{\frac{\alpha}{\beta}}

\theta = \frac{\alpha^2}{\beta} - \frac{\alpha^2}{2\beta} = \frac{\alpha^2}{2\beta}

Answer:

\theta = \frac{\alpha^2}{2\beta}

Hence, the correct option is C.

Go to Question:

Prev Question

Next Question