Question

Calculate the gravitational force of earth acting on an object weighting 10kg placed 1000km above the surface of earth.
(Mass of earth $=6\times {10}^{24}kg$ and radius of earth $=6.4\times {10}^{6}m$)

• A. $0.84\times {10}^{3}N$
• B. $0.72\times {10}^{2}N$
• C. $0.65\times {10}^{6}N$
• D. $0.42\times {10}^{4}N$

Answer 1

Answer: (B)

$0.72\times {10}^{2}N$

Given:
Mass of earth $=6\times {10}^{24}kg$
Mass of object $=10kg$
Distance of the object $=$ Radius of earth + distance from earth"s surface
$=6.4\times {10}^{6}m+1000km$
$=6.4\times {10}^{6}m+1\times {10}^{6}m$
$=7.4\times {10}^{6}m$
$G=6.7\times {10}^{-11}N{m}^{2}k{g}^{-2}$
By using the formula,
$F=G\frac{M\times m}{d^2}$
$F=\frac{6.7\times {10}^{-11}N{m}^{2}k{g}^{-2}\times 6\times {10}^{24}kg\times 10kg}{(7.4\times {10}^{6}m{)}^2}$
$F=\frac{40.2\times {10}^{14}N{m}^2}{54.76\times {10}^{12}{m}^2}$
$F=\frac{4\times {10}^{15}N}{5.5\times {10}^{13}}$
$F=0.72\times {10}^{2}N$
Thus, the force exerted by earth on the object is $0.72\times {10}^{2}N$