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Question: Two spheres each of mass M and radius \(\frac { \mathrm { R } } { 2 }\) are connected with a massle...

Two spheres each of mass M and radius R2\frac { \mathrm { R } } { 2 } are connected with a massless rod of length 2R as shown in the figure. What will be the moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod –

A

215\frac { 21 } { 5 } MR2

B

25\frac { 2 } { 5 }MR2

C

52\frac { 5 } { 2 } MR2

D

521\frac { 5 } { 21 } MR2

Answer

215\frac { 21 } { 5 } MR2

Explanation

Solution

I = I1 + I2 = 25M(R2)2+[25M(R2)2+M(2R)2]\frac { 2 } { 5 } \mathrm { M } \left( \frac { \mathrm { R } } { 2 } \right) ^ { 2 } + \left[ \frac { 2 } { 5 } \mathrm { M } \left( \frac { \mathrm { R } } { 2 } \right) ^ { 2 } + \mathrm { M } ( 2 \mathrm { R } ) ^ { 2 } \right]

= 215MR2\frac { 21 } { 5 } \mathrm { MR } ^ { 2 }