If the Earth were to suddenly contract to (1/n) th of its present radius without any change in its mass, the duration of the new day will be nearly

Question

If the Earth were to suddenly contract to (1/n) th of its present radius without any change in its mass, the duration of the new day will be nearly (A) 24/n hr (B) 24 n hr (C) 24/n2 hr (D) 24 n2 hr

Tardigrade Admin · Accepted Answer

From the conservation of momentum, we have I1 ω1=I2 ω2 Thus, we get (2/5) M R2((2 π/T1)) =(2/5) M (R2/n2)((2 π/T2)) Hence, we get T2=(T1/n2)=(24/n2) h

Q. If the Earth were to suddenly contract to $\frac{1}{n}$ th of its present radius without any change in its mass, the duration of the new day will be nearly

$24/ n h r$

$24 n h r$

$24/ n^{2} h r$

$24 n^{2} h r$

From the conservation of momentum, we have
$I_{1} ω_{1} = I_{2} ω_{2}$
Thus, we get $\frac{2}{5} M R^{2} (\frac{2 π}{T _{1}})$ $= \frac{2}{5} M \frac{R ^{2}}{n ^{2}} (\frac{2 π}{T _{2}})$
Hence, we get $T_{2} = \frac{T _{1}}{n ^{2}} = \frac{24}{n ^{2}} h$

Q. If the Earth were to suddenly contract to n1​ th of its present radius without any change in its mass, the duration of the new day will be nearly

24/nhr

24nhr

24/n2hr

24n2hr