Question

If both, the mass and the radius of the earth decrease by 1%, what will be the% change in the
gravitational acceleration ?

Answer 1

If both, the mass and the radius of the earth decrease by 1%, what will be the% change in the gravitational acceleration?

**Solution:**

Gravitation acceleration on the surface of the Earth is given by:

$$g = \frac {G M}{R ^ {2}}$$

Where G is the gravitational constant, M is mass of the Earth and R is the radius of the Earth.

According to the problem:

$$M _ {2} = 0. 9 9 M$$ $$R _ {2} = 0. 9 9 R$$

Thus:

$$g _ {2} = \frac {G * (0 . 9 9 M)}{(0 . 9 9 R) ^ {2}} = \frac {0 . 9 9}{(0 . 9 9) ^ {2}} \frac {G M}{R ^ {2}} = \frac {0 . 9 9}{(0 . 9 9) ^ {2}} * g \approx 1. 0 1 g$$

So in the gravitational acceleration will increase by approximately 1%.

**Answer:** the gravitational acceleration will increase by approximately 1%.