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Atoms And Molecules

Question
CBSEENSC9006109

The acceleration due to gravity at the moon's surface is 1.67 m/s2. If the radius of the moon is 1.74 x 106 m, calculate the mass of the moon. Use the known value of G.

Solution

Given comma space
Gravitational space constant comma space straight G space equals space 6.67 space cross times space 10 to the power of negative 11 end exponent Nm squared divided by kg squared

Acceleration space due space to space gravity comma space straight g space equals space 1.67 space straight m divided by straight s squared

Radius space of space the space moon comma space straight R space equals space 1.74 space cross times space 10 to the power of 6 straight m

Mass space of space the space moon space is space given space by comma space

space space space space space space space space space straight M space equals space gR squared over straight G
space space space space space space space space space space space space space equals space fraction numerator 1.67 space cross times space left parenthesis 1.74 space cross times space 10 to the power of 6 right parenthesis squared over denominator 6.67 space cross times space 10 to the power of negative 11 end exponent end fraction space
space space space space space space space space space space space space space equals space 7.58 space cross times space 10 to the power of 22 space kg. space Ans.