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3-2.Motion in Plane
medium
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
$\frac{{(a - b)\,a}}{2}$
B
$\frac{{{a^2}}}{{2b}}$
C
$\frac{{{a^2} - {b^2}}}{{2b}}$
D
$\frac{{{a^2} - {b^2}}}{{2a}}$
Solution
$w=a-b t=0$
$t=a / b$
$\theta=\int \omega d t=\int_{0}^{1}(a-b t) d t$
$=\left(a t-\frac{b t^{2}}{2}\right)_{0}^{a/b}$
$=a \cdot \frac{a}{b}-\frac{6}{2} \frac{a^{2}}{b^{2}}$
$=a^{2} / 2 b$
Standard 11
Physics
