If the earth is one-fourth of its present distance from the sun, the duration of the year will be changed to

Question

If the earth is one-fourth of its present distance from the sun, the duration of the year will be changed to (A) half of the present year (B) ((1th/4)) of the present year (C) ((1th/8)) of the present year (D) ((7th/8)) of the present year

Tardigrade Admin · Accepted Answer

From Kepler's law, T2 propto r3 Hence, ((T1/T2))2 =((r1/r2))3=((r/r / 4))3 (T1/T2) =(4)3 / 2 T2 =(T1/43 / 2) T2 =(T1/8)

Q. If the earth is one-fourth of its present distance from the sun, the duration of the year will be changed to

half of the present year

$(\frac{1 ^{t h}}{4})$ of the present year

$(\frac{1 ^{t h}}{8})$ of the present year

$(\frac{7 ^{t h}}{8})$ of the present year

$(\frac{1 ^{t h}}{16})$ of the present year

From Kepler's law,
$T^{2} \propto r^{3}$
Hence, $(\frac{T _{1}}{T _{2}})^{2} = (\frac{r _{1}}{r _{2}})^{3} = (\frac{r}{r /4})^{3}$
$\frac{T _{1}}{T _{2}} = (4)^{3/2}$
$T_{2} = \frac{T _{1}}{4 ^{3/2}}$
$T_{2} = \frac{T _{1}}{8}$

Q. If the earth is one-fourth of its present distance from the sun, the duration of the year will be changed to

half of the present year

(41th​) of the present year

(81th​) of the present year

(87th​) of the present year

(161th​) of the present year

From Kepler's law, T2∝r3 Hence, (T2​T1​​)2=(r2​r1​​)3=(r/4r​)3 T2​T1​​=(4)3/2 T2​=43/2T1​​ T2​=8T1​​

$(\frac{1 ^{t h}}{4})$ of the present year

$(\frac{1 ^{t h}}{8})$ of the present year

$(\frac{7 ^{t h}}{8})$ of the present year

$(\frac{1 ^{t h}}{16})$ of the present year

From Kepler's law,
$T^{2} \propto r^{3}$
Hence, $(\frac{T _{1}}{T _{2}})^{2} = (\frac{r _{1}}{r _{2}})^{3} = (\frac{r}{r /4})^{3}$
$\frac{T _{1}}{T _{2}} = (4)^{3/2}$
$T_{2} = \frac{T _{1}}{4 ^{3/2}}$
$T_{2} = \frac{T _{1}}{8}$