First slide

Universal law of gravitation

Question

The radius of the earth is about 6400km and that of mars is about 3200km. The mass of the earth is about 10 times that of mars. If an object weighs 200 N on the surface of earth its weight on the surface of mars would be

Easy

A

40N
B

80N
C

8N
D

20N

Solution

$\large F = \frac{{GMm}}{{{R^2}}} \Rightarrow F \propto \frac{M}{{{R^2}}}$
$\large \frac{{{F_1}}}{{{F_2}}} = \frac{{{M_1}}}{{{M_2}}} \times {\left( {\frac{{{R_2}}}{{{R_1}}}} \right)^2} \Rightarrow \frac{{200}}{{{F_2}}} = 10\left[ {\frac{{3200}}{{6400}}} \right]^2$
$\large {F_2} = 80N$

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