The gravitational self potential energy of a ball of mass density ρ and radius 2R in terms of E will be -
E(2R) = 32 E(R) = 32 E
We have the gravitational self potential energy of a solid ball of mass density ρ and radius R equals to E.
We have to calculate the gravitational self potential energy of a ball of mass density ρ and radius 2R in terms of E.
What is the formula to calculate the gravitational potential energy of a sphere of mass 'M' and radius 'R'?
The gravitational potential energy can be calculated using the following formula -
U = [tex]\frac{-3GM^{2} }{5R}[/tex]
According to the question -
Gravitational self potential energy of a solid ball of mass density ρ and radius R equals to -
E(R) = [tex]\frac{-3GM^{2} }{5R}[/tex]
Now, if we increase the radius to twice of its initial value, then mass of the ball will become -
M(2R) = [tex]\frac{4\rho\pi \times (2R)^{3} }{3}[/tex] = [tex]\frac{4\pi R^{3}\rho \times (2)^{3} }{3} = 2^{3} \times M[R][/tex]
Squaring both sides -
[tex]([M(2R)])^{2}[/tex] = [tex](8M(R))^{2} = 64 [M(R)]^{2}[/tex]
Gravitational self potential energy of a solid ball of radius 2R will be -
E(2R) = [tex]\frac{-3G(M[2R])^{2} }{2\times 5R}[/tex] = [tex]\frac{64}{2} E(R)[/tex]
E(2R) = 32 E(R)
Hence, the gravitational self potential energy of a ball of mass density ρ and radius 2R in terms of E will be -
E(2R) = 32 E(R) = 32 E
To solve more questions on gravitational potential energy of spheres, visit the link below -
https://brainly.com/question/27541711
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