Point masses mₐ and mᵦ are connected by a massless rod of length ℓ as shown. The moments of inertia about the parallel axes AA and BB, each perpendicular to the rod through the corresponding end, satisfy. $\frac{I_{BB}}{I_{AA}}$ =3. What is the distance of the centre of mass from mass mₐ?
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Question

Point masses mₐ and mᵦ are connected by a massless rod of length ℓ as shown. The moments of inertia about the parallel axes AA and BB, each perpendicular to the rod through the corresponding end, satisfy. $\frac{I_{BB}}{I_{AA}}$ =3. What is the distance of the centre of mass from mass mₐ?

Options

G1 Physics · Accepted Answer

About axis AA only mass mᵦ contributes, so I about AA=mᵦℓ². About axis BB only mass mₐ contributes, so I about BB=mₐℓ². Thus mₐ/mᵦ=3. The centre of mass measured from mₐ is x=mᵦℓ/(mₐ+mᵦ)=ℓ/4. Hence option D.