Q91 / 100 · BITSAT 2024 (Memory Based Paper 2) · Physics

The distance between Sun and Earth is $R$. The duration of year if the distance between Sun and Earth becomes $3 R$ will be:

A
$\sqrt{3}$ years
B
3 years
C
9 years
Correct answer
D
$3 \sqrt{3}$ years

Solution

Basically 1 year is equal to time period of earth revolution around sun. So, $T_i=1$ year Now, $T^2 \propto R^3$ $\therefore\left(\frac{T_2}{T_1}\right)^2=\left(\frac{R_2}{R_1}\right)^3$ $\Rightarrow T_2=\left(\frac{R_2}{R_1}\right)^{3 / 2} T_1=\left(\frac{3 R}{R}\right)^{3 / 2} \times 1$ $=3 \sqrt{3}$ years.

Hence, the correct answer is option: 'D'.

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