Question

4) On the moon's surface, the acceleration due to gravity is 1.67 ms-2. If the radius of the
moon is 1.74 x 106 m, calculate the mass of the moon. (G= 6.67 × 10^11 Nm2/kg 2)
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Answer 1

Answer:

g=1.67m/s sq.

R=1.74*10 to the power 6 m

M =?

we know , g=GM

___

R sq.

1.67=6.67*10 to the power -11*M

_____________________

(1.74*10 to the power 6) sq.

M =1.67*(1.74*10 to the power 6) sq.

_________________________

6.67*10 to the power -11

=1.67*1.74*1.74

___________ * 10 to the power 12+11

6.67

=0.758*10 to the power 33

=7.58*10 to the power 32 kg

Answer 2

Answer:

Solution

As, g=GMR2orM=gR2G

This relation is true not only to the earth but for any heavenly body which is assumed to be spherical

Now, g=1.67ms-2,R=1.74×106m

G=6.67×10-11Nm-2kg-2

∴ Mass of the moon, M=1.67×(1.74×106)26.67×10-11kg

=7.58×1022kg.