The moment of inertia of an angular wheel shown in figure is 3200 ${kgm}^{2}$ . If the inner radius is 5 cm and the outer radius is 20 cm, and the wheel
is acted upon by the forces shown, then the angular acceleration of the wheel is

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$10^{- 1}$ $rad / s^{2}$

$10^{- 2} rad / s^{2}$

$10^{- 3} rad / s^{2}$

$10^{- 4} rad / s^{2}$

answer is C.

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Detailed Solution

$τ = Iα \Rightarrow 10 \times \frac{20}{100} + \frac{9 \times 20}{100} - \frac{12 \times 20}{100} = 3200 α$

$\Rightarrow α = 10^{- 3} rad / s^{2}$

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