MCQ
A rigid body rotates about a fixed axis with variable angular velocity equal to $\alpha -\beta t$, where $t$ is time and $\alpha \,,\, \beta $ are constants. The angle (in radian) through which it rotates before its stops
  • $\frac{{{\alpha ^2}}}{{2\beta }}$
  • B
    $\frac{{{\alpha ^2} - {\beta ^2}}}{{2\alpha }}$
  • C
    $\frac{{{\alpha ^2} - {\beta ^2}}}{{2\beta }}$
  • D
    $\frac{{(\alpha  - \beta )\alpha }}{2}$

Answer

Correct option: A.
$\frac{{{\alpha ^2}}}{{2\beta }}$
a
$\omega=\alpha-\beta t$

Comparing with $\omega=\omega_{0}-\alpha \mathrm{t}$

Initial angular velocity $=\alpha$

Angular retardation $=\beta$

Also

$\Rightarrow$ Angle rotated before it stops is $\frac{\alpha^{2}}{2 \beta}$

${0=\alpha^{2}-2 \beta \theta}$

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