gracemconner5183 gracemconner5183
  • 30-11-2019
  • Physics
contestada

At what fraction of its current radius would the free-fall acceleration at the surface be three times its present value?

Respuesta :

Manetho
Manetho Manetho
  • 01-12-2019

Answer:

0.577

Explanation:

The initial weight is

mg= [tex]\frac{GMm}{r_1^2}[/tex].......................1

and the final weight is

[tex]3mg= \frac{GMm}{r_2^2}[/tex]......................2

now to calculate [tex]r_2/r_1[/tex]

now dividing equation 1 by equation 2 we get

[tex]\frac{1}{r_1^2}/\frac{1}{r_2^2}[/tex]= 1/3

[tex]\frac{r_2}{r_1} =\sqrt{\frac{1}{3} }[/tex]

[tex]\frac{r_2}{r_1}[/tex]=0.577

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