A certain object weighs 22.2 N on the surface of Earth. If the radius of the Moon is 0.276 times the radius of Earth and the mass of the Moon is 0.0123 times the mass of Earth, the object's weight on the surface of the Moon is approximately
A) 0.365 N.
B) 3.58 N.
C) 9.79 N.
D) 22.2 N.
E) 133 N.

Question

Quizplus · Accepted Answer

The weight of an object is given by the formula $w=mg$, where $w$ is weight, $m$ is mass and $g$ is acceleration due to gravity.

On Earth, we have $w=22.2$ N. On the Moon, we need to find the weight $w_m$.

The acceleration due to gravity on the Moon ($g_m$) can be found using the equation:  $$\frac{g_m}{g} = \left(\frac{r_m}{r}ight)^2\left(\frac{M}{M_m}ight)$$ where $r$ and $r_m$ are the radii of Earth and the Moon respectively, and $M$ and $M_m$ are the masses of Earth and the Moon respectively.

Substituting the values and solving for $g_m$, we get:

$$\frac{g_m}{9.81	ext{ m/s}^2} = \left(\frac{0.276}{1}ight)^2\left(\frac{1}{0.0123}ight)$$

$$g_m = 1.625	ext{ m/s}^2$$

Now, using $w=mg$, we can find the weight of the object on the Moon:

$$w_m = mg_m = (m/9.81	ext{ kg})(1.625	ext{ m/s}^2)$$

$$w_m = 0.166m	ext{ N}$$

Substituting $m$ from the given weight on Earth, we get:

$$w_m = 0.166	imes 2.26	ext{ N} \approx \boxed{	extbf{(B)}\ 3.58	ext{ N}}$$

A Certain Object Weighs 22