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"` |