Question

2. If the size of the Earth were to shrink (diameter decreases) overnight without any change in its
mass, would you get up in the morning and find yourself heavier or lighter or would you still
weigh the same? Give reasons for your answer.

Answer 1

Gravity on earth's surface:

$\implies \rm g = \dfrac {GM_e}{R^2}$

where $\ M_e = mass\: of\: earth\\ \: R = radius \: of\: earth$

Weight of person:

$\implies \rm W = mg$

$\implies \rm W = m\bigg( \dfrac {GM_e}{R^2}\bigg)$

Now it is given that;

• mass of the person(m), earth's mass is constant.
• only diameter/radius of earth gets change.

$\implies\rm W \propto \dfrac{1}{R^2}$

★ If radius gets decrease, the weight will increase by square of its times, since they are inversely proportional to each other.

★ After get up in morning he will find his weight gets increase or heavier .

Answer 2

Explanation:

Gravity on earth's surface:

$\implies \rm g = \dfrac {GM_e}{R^2}$

where $\ M_e = mass\: of\: earth\\ \: R = radius \: of\: earth$

Weight of person:

$\implies \rm W = mg$

$\implies \rm W = m\bigg( \dfrac {GM_e}{R^2}\bigg)$

Now it is given that;

mass of the person(m), earth's mass is constant.

only diameter/radius of earth gets change.

$\implies\rm W \propto \dfrac{1}{R^2}$

★ If radius gets decrease, the weight will increase by square of its times, since they are inversely proportional to each other.

★ After get up in morning he will find his weight gets increase or heavier .