Q.

From a uniform disc of mass M and radius R, a concentric disc of radius R/2 is cut out for the remaining angular disc. I1 is the moment of inertia about axis ‘1’, I2 about 2, I3 about ‘3’, and I4 about ‘4’. Axes ‘1’ and ‘2’ are perpendicular to the disc and ‘3’ and ‘4’ are in the plane of disc. Axes ‘2’, ‘3’ and ‘4’ intersect at a common point.
 

Question Image


 

 List - I List - II
A)I1 is equal toP)2132MR2
B)I2 is equal toQ)I1/2
C)I3 + I4 is equal toR)1532MR2
D)I2 – I3 is equal toS)1521MR2
 (A)(B)(C)(D)
1)RPPQ
2)PQRS
3)PQSR
4)QRQS

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a

2

b

1

c

3

d

4

answer is A.

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Detailed Solution

Total mass : M ; Mass of cutout portion :
m1=M4;I1=12MR212m1R2=1532MR2I2=I1+3M4R22=2132MR2 Also I3+I4=I2;I2=I1+3M4R22I3=I12+3M4R22I2I3=I12

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