Question

The acceleration due to gravity on the surface of earth is ‘g’ m/s². The magnitude of the acceleration due to gravity in m/s² on the surface of a planet whose mass and radius are half those of earth:
1. 4g
2. 2g
3. g / 2
4. 8g

Answer 1

Correct Answer - Option 2 : 2g

Concept:

Acceleration due to gravity:

• The acceleration achieved by any object due to the gravitational force of attraction by any planet is called acceleration due to gravity by the earth.
• As each planet has a different mass and radius so the acceleration due to gravity will be different for a different planet.
• Acceleration due to gravity of the earth having mass M is given by:

\(g = \frac{{GM}}{{{R^2}}}\)--- (1)

Calculation:

Given the mass of Planet M' (let) is half of earth M' = M / 2 

Given, the radius of Planet R is half of earth R' = R / 2

Then, the acceleration due to the gravity of the planet g' is given as 

\(g' = \frac{{GM'}}{{{R'^2}}}\)  -- (2)

Putting the values of M' and R' in the above equation, we get

\(g' = \frac{{G(M/2)}}{{{(R/2)^2}}}\)

\(\implies g' = \frac{{G(M/2)}}{{{(R^2/4)}}}\)

\(\implies g' = \frac{{2GM}}{{{(R^2)}}}\)

Putting (1) in (2) we get

⇒g' = 2g

So, the acceleration due to gravity on that planet is twice that of earth.

So, 2g is the correct option.