A rigid body rotates about a fixed axis with variable angular velocity equal to(a bt) at t where a and b are constants. The angle through which it rotates before it comes to rest is

\frac{a^{2}}{b}

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\frac{a^{2}}{2 b}

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\frac{a^{2}}{4 b}

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\frac{a^{2}}{2 b^{2}}

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Solution

The correct option is A $\frac{a^{2}}{2 b}$
$ω = a - b t = 0 t = a / b θ = \int ω d t = \int_{0}^{a b} (a - b t) d t = {[a t - \frac{b t^{2}}{2}]}_{0}^{a / b} = a . \frac{a}{b} - \frac{b}{2} [\frac{a^{2}}{b^{2}}] = \frac{a^{2}}{2 b}$

B is the correct option

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A rigid body rotates about a fixed axis with variable angular velocity equal to(a bt) at t where a and b are constants. The angle through which it rotates before it comes to rest is

The correct option is A a22bω=a−bt=0t=a/bθ=∫ωdt=∫ab0(a−bt)dt=[at−bt22]a/b0=a.ab−b2[a2b2]=a22b B is the correct option

The correct option is A $\frac{a^{2}}{2 b}$
$ω = a - b t = 0 t = a / b θ = \int ω d t = \int_{0}^{a b} (a - b t) d t = {[a t - \frac{b t^{2}}{2}]}_{0}^{a / b} = a . \frac{a}{b} - \frac{b}{2} [\frac{a^{2}}{b^{2}}] = \frac{a^{2}}{2 b}$

B is the correct option