Answer to Question #83629 in Physics for Elizabeth Wiseman

Question

You weigh 740 N.
What would you weigh if the Earth were
two times as massive as it is and its radius
were three times its present value?
Answer in units of N.

Answer 1

Answer on Question 83629, Physics, Other

Question:

You weigh

$$740 N$$

. What would you weigh if the Earth were two times as massive as it is and its radius were three times its present value? Answer in units of N.

Solution:

From the definition of the weight, we have:

$$W=mg$$

,

here,

$$m$$

is the mass of the person,

$$g$$

is the acceleration due to gravity.

By the definition of the acceleration due to gravity, we have:

$$g=GM_E/R_E^2$$

,

here,

$$G$$

is the universal gravitational constant,

$$M_E$$

is the mass of the Earth and

$$R_E$$

is the radius of the Earth.

Substituting the expression for

$$g$$

into the first equation, we get:

$$W=mg=mGM_E/R_E^2∝M_E/R_E^2$$

.

Then, we can find the new weight from the relationship:

$$Wnew/W=M_Enew/(R_Enew)^2/(M_E/R_E^2)$$

,

$$Wnew/W=2M_E/(3R_E)^2/(M_E/R_E^2)=2/9$$

.

Finally, we get:

$$Wnew=(2/9)W=(2/9)*740 N=164 N$$

.

Answer:

$$Wnew = 164 N$$

.