Question

Four masses of $1\text{kg}$ each are placed to form a square as shown. What will be the magnitude of work required to double the length of the square keeping the masses at the corners?

• A. $W=G\left(\frac{2\sqrt{2}+1}{\sqrt{2}}\right)$
  
• B. $W=G\left(\frac{2\sqrt{2}-1}{3\sqrt{2}}\right)$
• C. $W=G\left(\frac{2\sqrt{2}+1}{\sqrt{2}}\right)$
• D. $W=G\left(\frac{2\sqrt{2}-1}{\sqrt{2}}\right)$

Answer 1

The correct option is A $W=G\left(\frac{2\sqrt{2}+1}{\sqrt{2}}\right)$


$W=|\Delta U|=|U_f-U_i|$

$U_i=4(-\frac{Gmm}{r})+2(-\frac{Gmm}{\sqrt{2}r})$
$U_i=-G(4+\sqrt{2})$
$U_f=4(-\frac{Gmm}{r})+2(-\frac{Gmm}{\sqrt{2}r})$
$U_f=-G(2+\frac{1}{\sqrt{2}})$

$W=|\Delta U|=|U_f-U_i|$

$W=G\left(\frac{2\sqrt{2}+2-1}{\sqrt{2}}\right)W=G\left(\frac{2\sqrt{2}+1}{\sqrt{2}}\right)$