Answer to Question #191618 in Physics for Faisal

Question

Q 21) The average distance of earth from the sun is about 2.6 times greater than the distance from

Mercury to the sun. Mercury’s period of circulation around the sun is:

1) 1 month

2) 3 months

3) 0.5 years

4) 2 years

Answer 1

Apply Kepler's third law:

$$\frac{T^2_E}{T_M^2}=\frac{a_E^3}{a_M^3},\\\space\\ a_E=2.6a_M,\\\space\\ \frac{T^2_E}{T_M^2}=\frac{(2.6a_M)^3}{a_M^3},\\\space\\ T_M=\frac{T_E}{\sqrt{2.6^3}}=2.86\text{ months}.$$