Moment of inertia of a uniform disc of mass $m$ about an axis $x = a$ is $m k^{2}$ ,where $k$ is the radius of gyration. What is its moment of inertia about an axis $x = a + b$

m k^{2} - m a^{2} + m {(a + b)}^{2}

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m k^{2} + m \frac{(a + b)^{2}}{2}

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m k^{2} + m \frac{b^{2}}{2}

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m k^{2} + m b^{2}

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Solution

The correct option is A $m k^{2} - m a^{2} + m {(a + b)}^{2}$
$\begin{matrix} m K^{2} = I_{c m} = m a^{2} a b o u t x = (a + b) I = I_{c m} + n {(a + b)}^{2} = m k^{2} - m a^{2} + m {(a + b)}^{2} \end{matrix}$
$∴$ Option $A$ is correct .

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Moment of inertia of a uniform disc of mass m about an axis x=a is mk2,where k is the radius of gyration. What is its moment of inertia about an axis x=a+b

The correct option is A mk2−ma2+m(a+b)2mK2=Icm=ma2aboutx=(a+b)I=Icm+n(a+b)2=mk2−ma2+m(a+b)2∴ Option A is correct .

Moment of inertia of a uniform disc of mass $m$ about an axis $x = a$ is $m k^{2}$ ,where $k$ is the radius of gyration. What is its moment of inertia about an axis $x = a + b$

The correct option is A $m k^{2} - m a^{2} + m {(a + b)}^{2}$
$\begin{matrix} m K^{2} = I_{c m} = m a^{2} a b o u t x = (a + b) I = I_{c m} + n {(a + b)}^{2} = m k^{2} - m a^{2} + m {(a + b)}^{2} \end{matrix}$
$∴$ Option $A$ is correct .