What is the acceleration due to gravity on the surface of Mercury?

• A. $24.8m/s^2$
• B. $3.7m/s^2$
• C. $9.8m/s^2$
• D. $1.6m/s^2$

Answer: (B)

Verified step by step guidance

1. Understand that the acceleration due to gravity on the surface of a planet is given by the formula \(g = \frac{G M}{R^2}\), where \(G\) is the universal gravitational constant, \(M\) is the mass of the planet, and \(R\) is the radius of the planet.
2. Identify the known values for Mercury: its mass \(M_{Mercury}\) and radius \(R_{Mercury}\). These values are typically found in physics reference tables or textbooks.
3. Substitute the values of \(G\), \(M_{Mercury}\), and \(R_{Mercury}\) into the formula \(g = \frac{G M_{Mercury}}{R_{Mercury}^2}\) to calculate the acceleration due to gravity on Mercury.
4. Perform the calculation carefully, ensuring units are consistent (mass in kilograms, radius in meters, and \(G\) in \(\mathrm{m^3\,kg^{-1}\,s^{-2}}\)) to get \(g\) in \(\mathrm{m/s^2}\).
5. Compare the calculated value of \(g\) for Mercury with the given options to identify the correct acceleration due to gravity on Mercury's surface.