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6. system of particles and rotational motion — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics6. system of particles and rotational motion1 Mark
MCQ
A rigid body is rotating with variable angular velocity $(a - bt)$ at any instant of time $ t.$ The total angle subtended by it before coming to rest will be ($a$ and $b$ are constants)
  • A
    $\frac{{(a - b)\,a}}{2}$
  • ✓
    $\frac{{{a^2}}}{{2b}}$
  • C
    $\frac{{{a^2} - {b^2}}}{{2b}}$
  • D
    $\frac{{{a^2} - {b^2}}}{{2a}}$
✓

Answer

Correct option: B.
$\frac{{{a^2}}}{{2b}}$
b
$w=a-b t=0$

$t=a / b$

$\theta=\int \omega d t=\int_{0}^{1}(a-b t) d t$

$=\left(a t-\frac{b t^{2}}{2}\right)_{0}^{a/b}$

$=a \cdot \frac{a}{b}-\frac{6}{2} \frac{a^{2}}{b^{2}}$

$=a^{2} / 2 b$

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