You weigh 730N. What would you weigh if the earth were six times as massive as it is and its radius were four times its present

Question

3 years ago

13

value? Answer in units of N.

1 answer:

Ber [7] · Answer 1 · 2022-07-29T22:09:55+03:00

The new weight is 273.8 N

Explanation:

The weight of an object on Earth is given by

$W=mg$

where

m is the mass of the object

g is the acceleration of gravity

The acceleration of gravity at the Earth's surface can be rewritten as

$g=\frac{GM}{R^2}$

where

G is the gravitational constant

M is the Earth's mass

R is the Earth's radius

Substituting into the previous equation,

$W=\frac{GMm}{R^2}$

We said that in normal conditions, the weight of the person is 730 N:

$W=\frac{GMm}{R^2}=730 N$

Later, we are said that:

Substituting into the equation, we find the new weight of the person in these conditions:

$W'=\frac{G(6M)m}{(4R)^2}=\frac{6}{16}(\frac{GMm}{R^2})=\frac{3}{8}W$

So, the new weight is 3/8 of the original weight, therefore:

$W'=\frac{3}{8}(730)=273.8 N$

Learn more about gravity:

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