Two masses of 0.3 , kg and 0.7 , kg are attac | vedclass

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(B) The work done to rotate a body with constant angular velocity $\omega$ is given by $W = \frac{1}{2} I \omega^2$. For the work to be minimum,the mo

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$0.98 \, m$ from the $0.3 \, kg$ mass

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(B) The work done to rotate a body with constant angular velocity $\omega$ is given by $W = \frac{1}{2} I \omega^2$. For the work to be minimum,the moment of inertia $I$ of the system must be minimum.Let the axis of rotation be at a distance $x$ from the $0.3 \, kg$ mass. Then the distance from the $0.7 \, kg$ mass is $(1.4 - x)$.The moment of inertia $I$ is given by: $I = m_1 x^2 + m_2 (L - x)^2 = 0.3 x^2 + 0.7 (1.4 - x)^2$.To find the minimum $I$,we differentiate with respect to $x$ and set it to zero:$\frac{dI}{dx} = 0.3(2x) + 0.7(2)(1.4 - x)(-1) = 0$$0.6x - 1.4(1.4 - x) = 0$$0.6x - 1.96 + 1.4x = 0$$2.0x = 1.96$$x = 0.98 \, m$.Thus,the axis should pass at a distance of $0.98 \, m$ from the $0.3 \, kg$ mass.

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