BITSAT 2022 Paper

Area mass density, σ=

M

16R2

(∵Area=4R×4R=16R2)
Mass of each hole m1=σπR2=

M

16R2

πR2=

πM

16

Distance between centre of plate and centre of hole
x=

√(2R)2+(2R)2

2

=

2√2R

2

Moment of inertia of one hole at about Z-axis
I1=

1

2

m1R2+m1x2=

5π

32

MR2
Moment of inertia of whole plate about Z-axis,
I=

M(4R)2

6

=

8

3

MR2
Required moment of Inertia
I0=I−4I1,=[

8

3

−4(

5π

32

)]MR2=[

8

3

−

5π

8

]MR2
Given, R=5cm and M=1kg
So, I0[

8

3

−

5π

8

]1×25×10−4=0.0017kg−m2