A circular metal disc of mass 200g and radius 20 cm makes 10 revolutions per second about an axis passing through the centre and perpendicular to its plane .then the moment of inertia is about it axis is $4 \times 10^{- 3} {kgm}^{3}$ , the torque required to change its angular velocity from 10 rps to 20 rps in 5 seconds is $5 \times 10^{- x}$ ,the value of $x$ is _______

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answer is 2.

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Detailed Solution

$\begin{array}{l} τ = I α = I (\frac{ω_{2} - ω_{1}}{t}) \\ = 4 \times 10^{- 3} (\frac{40 π - 20 π}{5}) \Rightarrow 5 \times 10^{- 2} (Given τ = 5 \times 10^{- x}) \end{array}$
Hence x = 2

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