A solid sphere of mass m and radius R is rigidly enclosed in solid hollow shell of same mass m & radius R. This body is rolling down a rough incline of inclination #pi/4#.If minimum value of coefficient of static friction is #x/23#. Find value of #x#?

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Answer 1 · 2018-02-02T15:51:12

#8#

Please see the derivation below
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Here, #theta =45#, and moment of inertia #I =2/3 Mr^2+2/5 Mr^2# (hollow sphere+solid sphere) and mass #m=2M#

Putting the values,we get, #mu# greater or equal #8/23#

So, #x/23 = 8/23# or, #x=8#