Weight of 1 ,kg becomes 1/6 on moon. If radius of moon is 1.768 × {10^6},m , then mass of moon will

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7.Gravitation

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Weight of $1 \,kg$ becomes $1/6$ on moon. If radius of moon is $1.768 \times {10^6}\,m$, then the mass of moon will be

A

$1.99 \times {10^{30}}\,kg$

B

$7.56 \times {10^{22}}\,kg$

C

$5.98 \times {10^{24}}\,kg$

D

$7.65 \times {10^{22}}\,kg$

Solution

(d) ${g_m} = \frac{{G{M_m}}}{{R_m^2}}$ and ${g_m} = \frac{{{g_e}}}{6} = \frac{{9.8}}{6}\;m/{s^2}$$ = 1.63\;m/{s^2}$

Substituting ${R_m} = 1.768 \times {10^6}m,$ ${g_m} = 1.63\;m/{s^2}$ and $G = 6.67 \times {10^{ – 11}}N{\rm{ – }}{m^2}/k{g^2}$

We get ${M_m} = 7.65 \times {10^{22}}kg$

Standard 11

Physics

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