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Moment of Inertia Physics System of Particles and Rotational Motion Physics Class 11th

The linear mass density of a thin rod AB of length L varies from A to B as λ(x) = λ₀ (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 is:

Option 1 -

(5/12)ML²

Option 2 -

(7/18)ML²

Option 3 -

(2/5)ML²

Option 4 -

(3/5)ML²

4 Views | Posted a month ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 2

Detailed Solution:

dm = λdx = λ? (1 + x/L)dx
M = ∫? λ? (1 + x/L)dx = λ? [L + L²/2L] = 3λ? L/2
dI = dmx² = λ? (1 + x/L)dx × x²
I = λ? ∫? (x² + x³/L)dx = λ? [L³/3 + L? /4L]
I = (7λ? L³)/12 = (7/12) * (2M/3L) * L³ = (7/18)ML²

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The linear mass density of a thin rod AB of length L varies from A to B as λ(x) = λ₀ (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 is:

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