Question

in a hypothetical situation if mass of earth become 4 timed of original and radius become twicw then what will be the acc. due to gravity​

Answer 1

Correct question:-

In a hypothetical situation, if mass of earth becomes 4 times of original and radius becomes twice, the what will be the acceleration due to gravity?

Answer:-

Acceleration due to gravity remains the same or unchanged.

Explanation:-

We know that :-

gₑ = GMₑ/R²ₑ ------(1)

Where :-

• gₑ is the acceleration due to gravity on

the earth's surface.

• G is Universal Gravitational Constant.

• Mₑ is mass of the earth.

• Rₑ is the radius of the earth.

Now according to the question, mass of earth becomes 4 times i.e. 4Mₑ and radius of the earth becomes twice i.e. 2Rₑ. Hence, the equation for new acceleration due to gravity (g') will be :-

=> g' = G×4Me/(2Re)²

=> g' = 4GMₑ/4R²ₑ

=> g' = GMₑ/R²ₑ ----(2)

On dividing eq.2 by eq.1, we get :-

=> g'/gₑ = [GMₑ/R²ₑ]/[GMₑ/R²ₑ]

=> g'/gₑ = 1

=> g' = gₑ

Answer 2

Answer:

The weight of an object is directly proportional to the mass of the earth and inversely proportional to the square of the radius of the earth. i.e.,

If the diameter becomes half, the radius of the earth will also become half. So, they have the same relation.

Weight of a body ∝

R

2

M

Original weight W

0

=mg=mG

R

2

M

When hypothetically m becomes 4m and R becomes

2

R

Then weight becomes W

n

=mG

(

2

R

)

2

4M

=(16mG)

R

2

M

=16×W

0