Question

Suppose the mass of the earth somehow increases by 10 per cent without any change in its size. What would happen to your weight? Suppose the radius of the earth becomes twice its present radius without any change in its mass. What will happen to your weight?

Answer 1

Hey mate,

W = Force of gravity,

W = GMm/r^2 = mg

clearly if Mass is increased by 10% then Weight will be increased by 10 % as they r directly proportional .

W is inversely proportional to R^2 so if r is doubled then our mass will be W/4.

hope this helps you out!

Answer 2

Answer:

The increase in our weight in the first case will be 10 % and in the second case, our weight will reduce to one-fourth of the total.

Explanation:

Here we have been given that the mass of Earth somehow increases by 10% without having any change in its original size. Now as we know that the weight or the force of our body is given by the following formula;

$F = \frac{GMm}{R^{2} }$ = Weight (W)

Here we have F to be the force or the weight of the body, G is the universal gravitation constant, m here is the mass of our body and M is the mass of Earth.

Now we have been mentioned that only the mass of earth has increased and all other parameters are constant, therefore,

W ∝ M

Hence our weight will also increase by 10 %

Now further it has been mentioned that the radius of the Earth becomes twice the previous amount keeping the mass the same.

So for this, we have,

W ∝ $\frac{1}{R^{2} }$

The weight is inversely proportional to the square of the radius of our Earth.

Therefore let be $W_{1}$ the initial weight and $W_{2}$ be the final weight.

$R_{1}$ be the initial radius and $R_{2}$ be the final radius hence we have,

$\frac{W_{1} }{W_{2} } = (\frac{R_{2} }{R_{1} } )^{2}$

$R_{2} = 2 R_{1}$

Putting the values we get,

⇒ $\frac{W_{1} }{W_{2} } = (\frac{2R_{1} }{R_{1} } )^{2}$

⇒ $\frac{W_{1} }{W_{2} } =2^{2}$

⇒ $\frac{W_{1} }{W_{2} } =4$

⇒ $W_{2}= \frac{W_{1} }{4}$

Hence our weight will reduce to one-fourth times or in other words it will become one-fourth times the initial weight of our body.