First slide

Gravitational field intensity

Question

The moon's radius is 1/4 that of the earth and its mass is 1/80 times that of the earth. If g represents the acceleration due to gravity on the surface of the earth, that on the surface of the moon is

Moderate

A

g/4
B

g/5
C

g/6
D

g/8

Solution

$U \sin g g_{e} = \frac{G M}{R^{2}} g_{m} = \frac{G M_{m}}{{R_{m}}^{2}} = \frac{G \frac{M}{80}}{{(\frac{R}{4})}^{2}} = \frac{G \frac{M}{80}}{\frac{R^{2}}{16}} = \frac{G M}{R^{2}} \times \frac{16}{80} = g \times \frac{1}{5}$

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