The distance between centre of the earth and moon is 384000 km. If the mass of the earth is 6 × 1024 kg and G = 6.66 × 10–11 Nm2/kg2. The speed of the moon is nearly Option 1) 1 km/sec Option 2) 4 km/sec Option 3) 8 km/sec Option 4) 11.2 km/sec

As we learnt in

Orbital velocity of satellite -

$V=\sqrt{\frac{GM}{r}}$

$r=R+h$

$r\rightarrow$ Position of satellite from the centre of earth

$V\rightarrow$ Orbital velocity

- wherein

The velocity required to put the satellite into its orbit around the earth.

$\frac{mv^{2}}{R}=\frac{GmM_{e}}{R^{2}}\ \: \: or\ \: \: \: v=\sqrt{\frac{GM_{e}}{R}}$

$G=6.66\times 10^{-11},\ \: \: \: M_{e}=6\times 10^{24},\ \: \: R=384000\ km$

$v= 1 km/sec$

Option 1)

1 km/sec

This is correct option

Option 2)

4 km/sec

This is incorrect option

Option 3)

8 km/sec

This is incorrect option

Option 4)

11.2 km/sec

This is incorrect option

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