Question

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

• A. Half the present year
• B. One eighth of the present year
• C. One fourth of the present year
• D. One sixth of the present year

Answer 1

Answer: (B)

One eighth of the present year

According to Kepler's law

$T^2\alpha R^3$

$T=K{R}^3$

Where $R$ is the distance from sun to earth.

Here,

$T_1^2=K{R}_1^3$

$T_2^2={KR}_2^3$

Now, $R_2=\frac{R_1}{4}$

So, $T_2^2=\frac{K{R}_1^3}{64}$

$\frac{T_1^2}{T_2^2}=64$

$T_1=8T_2$

$T_2=\frac{T_1}{8}$