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Q.

A metal piece of mass 120 gm is stretched into a thin plane rectangular sheet of area of cross-section 0.54 m2 . If the length and breadth of this sheet are in the ratio 1:6, the moment of inertia about an axis passing through its centre and perpendicular to its plane is

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a

3.3kg m2

b

3.3×10−2kg m2

c

6.6×10−2kg m2

d

6.6kg m2

answer is B.

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Detailed Solution

I=m12(ℓ2+b2) A=ℓb   and ℓb=16 b=6ℓ A=ℓb=6ℓ2 0.54=6ℓ2 ℓ=0.3 I=Mℓ2+b212=0.120.32+1.8212=3.3×10−2kg m2 .
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A metal piece of mass 120 gm is stretched into a thin plane rectangular sheet of area of cross-section 0.54 m2 . If the length and breadth of this sheet are in the ratio 1:6, the moment of inertia about an axis passing through its centre and perpendicular to its plane is