A mass of 1kg on earth weighs 1-6 kg on moon- The radius of the moon is 1-738- 106m- The mass of the moon is g e-9-8m-s2-G-6-67- 10-11Mn2-kg2

The correct option is A 7.4× 10^22 kg [ GMe / Re ^ 2 = 6GMm / R m^ 2 =9.8; ⇒ Mm= 9.8× R m^ 2 6G ...

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Standard IX

Physics

Acceleration Due to Gravity

A mass of 1kg...

Question

A mass of 1kg on earth weighs ( 1/6) kg on moon. The radius of the moon is $1.738 \times 10^{6}$ m. The mass of the moon is ( g $_{e} = 9.8 m / s^{2}, G = 6.67 \times 10^{- 11} M n^{2} / k g^{2}$ )

7.4 \times 10^{22}

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4.35 \times 10^{16}

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4.4 \times 10^{23}

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7.4 \times 10^{20}

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Solution

The correct option is A $7.4 \times 10^{22}$ kg
$\begin{matrix} \frac{G M e}{{R e}^{2}} = \frac{6 G M m}{R m^{2}} = 9.8 \Rightarrow M m = \frac{9.8 \times R m^{2}}{6 G} = \frac{9.8 \times 1.738 \times 1.738 \times 10^{12}}{6 \times 6.67 \times 10^{- 11}} = 0.7396 \times 10^{23} H e n c e, o p t i o n A i s c o r r e c t a n s w e r . \end{matrix}$

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A mass of 1kg on earth weighs ( 1/6) kg on moon. The radius of the moon is 1.738×106m. The mass of the moon is ( ge=9.8m/s2,G=6.67×10−11Mn2/kg2)

The correct option is A 7.4×1022kgGMeRe2=6GMmRm2=9.8⇒Mm=9.8×Rm26G=9.8×1.738×1.738×10126×6.67×10−11=0.7396×1023Hence,optionAiscorrectanswer.

A mass of 1kg on earth weighs ( 1/6) kg on moon. The radius of the moon is $1.738 \times 10^{6}$ m. The mass of the moon is ( g $_{e} = 9.8 m / s^{2}, G = 6.67 \times 10^{- 11} M n^{2} / k g^{2}$ )