Question 246: Gravitation

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 $${x \over 5}{{G{M^2}} \over R}$$ where x is __________ (Round off to the Nearest Integer) (M is the mass of earth, R is the radius of earth, G is the gravitational constant)

Accepted Answer

We know that binding energy of earth,
$$BE =  - {3 \over 5}{{G{M^2}} \over R}$$
$$	herefore$$ Energy required to break the earth into pieces
$$ =  - BE = {3 \over 5}{{G{M^2}} \over R}$$ ...... (i)
According to question, the amount of energy that needs to be supplied is $${x \over 5}{{G{M^2}} \over R}$$.
Comparing it with value in Eq. (i), we get,
$$x = 3$$

Gravitation

Integer / Numeric Answer Type