if mass of earth decreases by 25% and its radius increases by 50% then acc. due to gravity at its surface decreases by nearly......in %.…...?????plzzz reply as soon as.....

Question

Answer

Given:

Mass of Earth decreases by 25%
Radius of Earth increases by 50%

To find:

Percentage decrease in acceleration due to gravity at the surface of the Earth

Solution:

The acceleration due to gravity at the surface of the Earth is given by the formula:

g = GM/r^2

Where:
g = acceleration due to gravity
G = gravitational constant
M = mass of Earth
r = radius of Earth

Step 1: Calculate the new values of mass and radius

Let's assume the initial mass of Earth as M0 and the initial radius as r0.
The new mass of Earth after a 25% decrease is:
M' = M0 - (25/100) * M0 = 0.75 * M0

The new radius of Earth after a 50% increase is:
r' = r0 + (50/100) * r0 = 1.5 * r0

Step 2: Calculate the new acceleration due to gravity

Using the formula mentioned earlier, let's calculate the new acceleration due to gravity, g':

g' = GM'/r'^2

Substituting the new values:
g' = G * (0.75 * M0) / (1.5 * r0)^2
= G * 0.75 * M0 / (2.25 * r0^2)

Simplifying the equation:
g' = (0.75/2.25) * (G * M0 / r0^2)
= (1/3) * g

Step 3: Calculate the percentage decrease in acceleration due to gravity

The percentage decrease in acceleration due to gravity can be calculated using the formula:

% decrease = (Initial value - Final value) / Initial value * 100

Substituting the values:
% decrease = (g - g') / g * 100
= (g - (1/3) * g) / g * 100
= (2/3) * g / g * 100
= 200/3
≈ 66.67%

Therefore, the acceleration due to gravity at the surface of the Earth decreases by approximately 66.67%.

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