If the earth were to contract such that its radius becomes one quarter, without change in its mass, the duration of one full day would be

Question

If the earth were to contract such that its radius becomes one quarter, without change in its mass, the duration of one full day would be (A) 3 h (B) 1.5 h (C) 6 h (D) 4 h

Tardigrade Admin · Accepted Answer

As angular momentum is conserved, so Iω =constant ∴ I2ω 2=I1ω 1 Or (2/5)M( (R/4) )2× (2π /T)=(2/5)MR2× (2π /24) Or 16T=24 ⇒ T=1.5h

Q. If the earth were to contract such that its radius becomes one quarter, without change in its mass, the duration of one full day would be

3 h

1.5 h

6 h

4 h

2 h

As angular momentum is conserved, so
$I ω = co n s t an t$
$∴$ $I_{2} ω_{2} = I_{1} ω_{1}$
Or $\frac{2}{5} M (\frac{R}{4})^{2} \times \frac{2 π}{T} = \frac{2}{5} M R^{2} \times \frac{2 π}{24}$
Or $16 T = 24$
$\Rightarrow$ $T = 1.5 h$

Q. If the earth were to contract such that its radius becomes one quarter, without change in its mass, the duration of one full day would be

3 h

1.5 h

6 h

4 h

2 h

As angular momentum is conserved, so Iω=constant ∴ I2​ω2​=I1​ω1​ Or 52​M(4R​)2×T2π​=52​MR2×242π​ Or 16T=24 ⇒ T=1.5h

As angular momentum is conserved, so
$I ω = co n s t an t$
$∴$ $I_{2} ω_{2} = I_{1} ω_{1}$
Or $\frac{2}{5} M (\frac{R}{4})^{2} \times \frac{2 π}{T} = \frac{2}{5} M R^{2} \times \frac{2 π}{24}$
Or $16 T = 24$
$\Rightarrow$ $T = 1.5 h$