Question

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 value? Answer in units of N.

Answer 1

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:

• The mass of the Earth increases by a  factor of 6, $M'=6M$
• The radius of the Earth increases by a factor of 4, $R'=4R$

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:

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

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