Question

How much energy is needed to move a body of ${10}^{3}kg$ mass from Earth's surface to a height of $2R_E$?$(R_E=radiusofEarth=6400km)$

• A. $42\times {10}^{9}J$
• B. $36\times {10}^{9}J$
• C. $64\times {10}^{3}J$
• D. $84\times {10}^{3}J$

Answer 1

The correct option is A $42\times {10}^{9}J$

$U_i=-\frac{GMm}{R}$
$U_f=-\frac{GMm}{3R}$
$\Delta U=U_f-U_i=\frac{GMm}{R}-\frac{GMm}{3R}=\frac{2GMm}{3R}=\frac{2}{3}\frac{GM}{R^2}mR$
$=\frac{2}{3}mRg=\frac{2}{3}\times {10}^3\times 6400\times {10}^3\times 10=42.67\times {10}^{9}J$