Question

If the earth were to suddenly contract to half of its present radius ( without any
external torque on it ), by what duration would the day be decreased ? Assume
earth to be a perfect solid sphere of moment of inertia 2/5 MR2 .​

Answer 1

Answer:

Given,

r

2

=

2

1

r

1

m

1

=m

2

=m(say)

T

1

=24hr

By the conservation of angular momentum,

I

1

ω

1

=I

2

ω

2

. . . . . . . . .(1)

Where, ω=

T

2π

angular velocity of the earth

I=

5

2

mr

2

moment of inertia of earth.

From equation (1),

5

2

mr

1

2

.

T

1

2π

=

5

2

mr

2

2

.

T

2

2π

r

1

2

.

T

1

1

=r

2

2

.

T

2

1

T

1

T

2

=(

r

1

r

2

)

2

=(

r

1

r

1

/2

)

2

=

4

1

T

2

=T

1

.

4

1

T

2

=

4

24

hr=6hr

Answer 2

Answer:

first of all things a well destroyed by the gravity and use layer of atmosphere will escape from the Earth gravity. creature will survive.

But we think that it is happening slowly so

the gravity which change into 4.7 m/s.

and our weight will half