The linear mass density of a thin rod AB of length L varies from A to B as λ x = λ 0 1 + x L , where x is the distance from A . If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicul

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The linear mass density of a thin rod AB of length L varies from A to B as &#955; x = &#955; 0 1 + x L , where x is the distance from A . If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod :

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Correct answer: B. 7 18 ML 2

dm = &#955; . dv dI = dm . x 2 = &#955; 0 1 + x L . x 2 dx I = &#955; 0 &#8747; 0 1 x 2 + x 3 L dx = &#955; 0 x 3 3 + x 4 4 L 0 L = &#955; 0 L 3 3 + L 3 4 I = 7 &#955; 0 L 3 12 m = &#8747; 0 L &#955;dx = 3 &#955; 0 L 2 I m = 7 L 2 12 &#215; 3 2 = 7 L 2 18 &#8658; I = 7 18 mL 2

The linear mass density of a thin rod AB of length L varies from A to B as λ x = λ 0 1 + x L , where x is the distance from A . If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod :

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More from Rotational Motion

The linear mass density of a thin rod AB of length L varies from A to B as &#955; x = &#955; 0 1 + x L , where x is the distance from A . If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod :

Options

Correct answer

Step-by-step solution

More from Rotational Motion

The linear mass density of a thin rod AB of length L varies from A to B as λ x = λ 0 1 + x L , where x is the distance from A . If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod :