Question

If radius of earth shrinks by
0.1% without change in its
mass, the percentage
change in the duration of
one day​

Answer 1

Explanation:

Let the initial radius be r and final is r

2

=0.999r

Now using the angular momentum conservation

I

1

ω

1

=I

2

ω

2

We get 2mr

2

/5×ω

1

=2mr

2

2

/5×ω

2

So

ω

2

ω

1

=

1000

2

(999)

2

=0.998....(1)

T

initial

=2π/ω

1

,

T

final

=2π/ω

2

So

T

initial

T

final

=

ω

2

ω

1

from equation 1, decrease in time period is (1−0.998)×100=0.2%