Question

Supposing the earth suddenly contracts to half of its radius, what will be the length of the day?

• A. $12$ hours
• B. $8$ hours
• C. $6$ hours
• D. No change

Answer 1

The correct option is C $6$ hours

Angular velocity of earth $W=\frac{2\pi }{T}$

$T=24hrsV=RWV=R\frac{2\pi }{T}=\frac{2\pi R}{T}$

Rotational velocity remains same but $R$ becomes $2R$ then new time period of earth rotation will be $T^1$.

$V=\frac{2\pi R}{T}⟶\left(1\right)$

$V=\frac{2\pi R}{{2T}^1}⟶\left(2\right)$

Dividing eq $\left(1\right)$ by eq $\left(2\right)$

$T^1=6hrs$.