Question

In analyzing distances by apply ing the physics of gravitational forces, an astronomer has obtained the expression
R= √1/([1/140×10^9 meter]^2 - [1/208×10^9]^2)
Use your calculator to evaluate R. View Available Hint(s)
(A) 3.87 x 10-12 meter
(B) 1.72× 1011 meter
(C) 2.58 x 1011 meter
(D) 1.49 x 1011 meter

Answer 1

Explanation:

It is given that, in analyzing distances by applying the physics of gravitational forces, an astronomer has obtained the expression as :

We need to evaluate the value of R using calculator.

$R=\sqrt{\dfrac{1}{(\dfrac{1}{149\times10^9\ })^2-(\dfrac{1}{208\times10^9\ })^2}}$..............(1)

$(\dfrac{1}{140\times10^9\ })^2=5.10\times 10^{-23}$

$(\dfrac{1}{208\times10^9\ })^2=2.31\times 10^{-23}$

On solving equation (1) we get the value of R as :

$R=2.13\times 10^{11}\ meter$

So, the calculated distance from above expression is $2.13\times 10^{11}\ meter$. Hence, this is he required solution.  

Answer 2

Answer : The correct value of R is, $1.89\times 10^{11}m$

Explanation :

The given expression is:

$R=\sqrt{\frac{1}{(\frac{1}{140\times 10^9m})^2-(\frac{1}{208\times 10^9m})^2}}$

$R=\sqrt{\frac{1}{(7.143\times 10^{-12})^2-(4.808\times 10^{-12})^2}}$

$R=\sqrt{\frac{1}{(5.102\times 10^{-23})-(2.312\times 10^{-23})}$

$R=\sqrt{\frac{1}{(2.79\times 10^{-23})}$

$R=\sqrt{(3.584\times 10^{22})}$

$R=1.89\times 10^{11}m$

Therefore, the value of R is, $1.89\times 10^{11}m$