Question

If radius of earth is increased, without chage in its mass, will the length of day increase, decrease or remain same?

Answer 1

I will increase

∴ω will decrease (as Iω= constant)

∴T will increase (as T=2π/ω)

Answer 2

The length of day would :

• We know that, moment of inertia is directly proportional to the square of the radius of an object.

i.e moment of inertia for sphere,

I = (2/5)×mR^2

• As radius increases, moment of inertia also increases.

• Also, Angular momentum is conserved.

i.e I×w = constant

where w = angular frequency

• But we already know that I is increasing, so to keep angular momentum conserved w has to decrease.

• Time period is given as,

T = 2×pi/w

• Hence w decreases, Time period increases

• Therefore, the length of day would increase