Question

If the radius of earth contracts to half of its value today, (the mass remaining unchanged), then the duration of the day will be ____________.

Options

• 48 hrs

• 24 hrs

• 12 hrs

• 6 hrs

Answer 1

If the radius of earth contracts to half of its value today, (the mass remaining unchanged), then the duration of the day will be 6 hrs.

Explanation:

`"L"_1 = "I"_1  omega_1 = 2/5 "MR"^2  omega_1`      .....(i)

Now its radius becomes half without change in its mass

`"L"_2 = "I"_2  omega_2 = 2/5 "M" ("R"/2)^2 omega_2`     ....(ii)

Let angular momentum be conserved,

L₁ =L₂

`"Hence,"  2/5 "MR"^2 omega_1`

` = 1/4 xx 2/5 "MR"^2 omega_2`

`"i.e."  omega_2 = 4 omega_1`

`"T"_2/"T"_1 = omega_1/omega_2 = 1/4`

`"T"_2 = "T"_1/4 = 24/4`

` = 6  "hours"`