AP EAPCET 07-Jul-2022 Shift 1 Paper

If earth shrinks to

1

64

of its original volume;

4

3

πr3=

1

64

(

4

3

πR3)
Here, r= new radius and R= original radius
⇒r3=

R3

64

or r=

R

4

As there is no external torque, angular momentum of earth remains constant
i.e., I1ω1=I2ω2 ...[∵Isphere=

2

5

MR2]
⇒

2

5

MR2⋅

2π

T1

=

2

5

Mr2

2π

T2

...[∴ω=

2π

T

,T=time‌of‌revolution‌about‌axis]
⇒T2=

r2T1

R2

⇒T2=

R2 16 ×T1

R2

...[∴r=

R

4

]
⇒T2=

T1

16

=

24

16

h
or T2=1.5h