Three solid spheres each of mass m and diameter d are stuck together such that the lines connecting the centres form an equilateral triangle of side of length d . The ratio I 0 I A of moment of inertia I 0 of the system about an axis passing the centroid and about center of any of the spheres I A and perpendicular to the plane of the triangle is:

M.I about O = 3 2 5 M d 2 2 + M d 3 2 = 13 10 M d 2 M.I about A = 2 2 5 M d 2 2 + M d 2 + 2 5 M d 2 2 = 23 10 M d 2 Now ratio = 13 23

Physics - Rotation Question with Solution | TestHub

PhysicsRotationCalculation of M.I.Easy2 minPYQ_2020

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Three solid spheres each of mass $m$ and diameter $d$ are stuck together such that the lines connecting the centres form an equilateral triangle of side of length $d$ . The ratio $\frac{I_{0}}{I_{A}}$ of moment of inertia $I_{0}$ of the system about an axis passing the centroid and about center of any of the spheres $I_{A}$ and perpendicular to the plane of the triangle is:

Options:

Answer:

Solution:

M.I about O $= 3 [\frac{2}{5} M {(\frac{d}{2})}^{2} + M {(\frac{d}{\sqrt{3}})}^{2}] = \frac{13}{10} M d^{2}$
M.I about A $= 2 [\frac{2}{5} M {(\frac{d}{2})}^{2} + M {(d)}^{2}] + \frac{2}{5} M {(\frac{d}{2})}^{2} = \frac{23}{10} M d^{2}$
Now ratio $= \frac{13}{23}$

Stream:JEESubject:PhysicsTopic:RotationSubtopic:Calculation of M.I.

⏱ 2mℹ️ Source: PYQ_2020

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