Question

If the force of gravity between a book of mass 0.50 kg and a calculator of 0.100 kg is 1.5 × 10-10 N, how far apart are they?

Answer 1

$m_1=0,5kg \\ m_2=0,1kg \\ F=1,5*10^{-10}N \\ G=6,67*10^{-11}m^3/kg*s^2 \\ \\ r=? \\ \\ \\ F= \frac{Gm_1m_2}{r^2 } \\ \\ Fr^2=Gm_1m_2 \\ \\r^2=\frac{Gm_1m_2}{F} \\ \\ r= \sqrt{\frac{Gm_1m_2}{F} } =$

$=\sqrt{ \frac{6,67*10^{-11} \frac{m^3}{kg*s^2}*0,5kg*0,1kg }{1,5*10^{-10}N} } = \sqrt{ \frac{6,67*10^{-11} \frac{m^3}{kg*s^2}*0,05kg^2 }{1,5*10^{-10} \frac{kg*m}{s^2} } } = \\ \\ =\sqrt{ \frac{6,67 *10^{-11}*0,05 }{1,5*10^{-10}}m^2 } \approx\boxed{0,15m} \\ \\ \\ \\ \\ \\ "Non\ nobis,\ Domine,\ non\ nobis,\ sed\ Nomini\ tuo\ da\ gloriam." \\ \\ \\ \\ \underline{\underline{Regards\ M.Y.}}$