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Question

# If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be $\frac{x}{5}$$\frac{G{M}^{2}}{R}$ where x is __________. (Round off to the Nearest Integer). (M is the mass of the earth, R is the radius of the earth, and G is the gravitational constant)

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Solution

## Step 1: Given data:${U}_{i}$ = Self-potential energy of the earthG = Universal gravitational consatntM = Mass of the earthR = Radius of the earthStep 2: Calculating the value of xThe self-potential energy of the earth is shown as follows.${U}_{i}=-\frac{3G{M}^{2}}{5R}$ â€¦â€¦â€¦(1)But when all the mass above the earth is removed in infinity, its potential energy will be as follows.${U}_{f}=0$ â€¦â€¦â€¦(2)So,$E={U}_{f}-{U}_{i}$$E=0-\left(-\frac{-3G{M}^{2}}{5R}\right)$$E=\frac{3G{M}^{2}}{5R}$ â€¦â€¦â€¦..(3)As per the information given in the question.$E=\frac{x}{5}\frac{G{M}^{2}}{5R}$ â€¦â€¦.â€¦.(4)When we get the equations (3) and (4) together.$\frac{x}{5}\frac{G{M}^{2}}{R}=\frac{3G{M}^{2}}{5R}$$X=3$So here x is equal to 3.

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