NEET 2025 — Physics solution

NEET2025Physics

The radius of Martian orbit around the Sun is about $4$ times the radius of the orbit of Mercury. The Martian year is $687$ Earth days. Then which of the following is the length of $1$ year on Mercury?

A
88 earth days
B
225 earth days
C
172 earth days
D
124 earth days

Solution

Kepler's third law: $T^{2} \propto r^{3}$ , so $\frac{T _{M er c u r y}}{T _{M a r s}} = (\frac{r _{M er c u r y}}{r _{M a r s}})^{3/2} = (\frac{1}{4})^{3/2} = \frac{1}{8}$ .

$T_{M er c u r y} = \frac{687}{8} \approx 85.9 \approx 88$ earth days.

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